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    (Original post by Chittesh14)
    Erm, well I can't really factorise it so let's just go with my favourite method lol.
    (x+1)^2 - 1 + 2 = 0

(x+1)^2 + 1 = 0

(x+1)^2 = -1

    Well, you can't complete the square either .

    Well, the quadratic formula doesn't work either wtf lol, this equation has no solutions.
    b^2 - 4ac = 4 - 8 = -4

b^2 - 4ac < 0 so there are no real roots.

    Apparently, the solutions (roots) are imaginary lol so the graph does not cross the x-axis.
    I tried WolframAlpha and it says -1 + i and -1 - i.
    I don't know what that means lol :/ sorry I can't help :'(.

    Btw, what year are you in? - just wondering
    Ah damn.
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    In all honesty, I knew the solutions. I just wanted to see how you would react to it.
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    (Original post by RDKGames)
    Ah damn.
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    In all honesty, I knew the solutions. I just wanted to see how you would react to it.
    Lol, I thought so. Cheeky.
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    (Original post by Chittesh14)
    Lol, I thought so. Cheeky.
    To answer your question, I'm on the verge of finishing Y13 with 2 exams left. Taken Maths and Further Maths.
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    (Original post by RDKGames)
    To answer your question, I'm on the verge of finishing Y13 with 2 exams left. Taken Maths and Further Maths.
    Oh wow, good luck .
    How did the previous exams go?
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    (Original post by Chittesh14)
    Oh wow, good luck .
    How did the previous exams go?
    Thanks! ;D

    Well I have 10 exams overall this summer, all maths incl. 3 retakes. All went well except maybe C3, and I had my worst exam ever in maths with Mechanics 3 this year. I'm yet to find a single person who enjoyed that exam. Otherwise, they're not too bad and if I'm lucky Loughborough might even accept me with my grades being one lower than expected xD
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    (Original post by RDKGames)
    Thanks! ;D

    Well I have 10 exams overall this summer, all maths incl. 3 retakes. All went well except maybe C3, and I had my worst exam ever in maths with Mechanics 3 this year. I'm yet to find a single person who enjoyed that exam. Otherwise, they're not too bad and if I'm lucky Loughborough might even accept me with my grades being one lower than expected xD
    Wow nice man! Quite a lot of exams :P. If you don't mind me asking, what were your 3 retakes and what grades did you get at AS in your subjects? What is your offer for Loughborough btw? And dam, sorry about M3 - I don't think I know anybody doing it lol in my school, except one person maybe. Well, really I think you'd have done good in all - but the extra 3 retakes might've put a bit more pressure so you've actually done really good :P
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    (Original post by Chittesh14)
    Wow nice man! Quite a lot of exams :P. If you don't mind me asking, what were your 3 retakes and what grades did you get at AS in your subjects? What is your offer for Loughborough btw? And dam, sorry about M3 - I don't think I know anybody doing it lol in my school, except one person maybe. Well, really I think you'd have done good in all - but the extra 3 retakes might've put a bit more pressure so you've actually done really good :P
    My retakes were Core 1 (orginally B), FP1 (originally B) and S1 (originally D) and this year I think they went far better so I can balance out my AS Further Maths at an A. My Loughborough offer is AAA for studying Mathematics but at this rate I should be getting A*A*B, if not Loughborough then I'm off to Leicester aha. I don't mind M3 as I'm doing an extra module which would replace it (which is D2) given that it goes better than M3, which most likely will lol but I still need to do good in it xD

    Also retakes are absolutely no pressure really, C1 and FP1 were naturally covered as I worked through C3 and C4 as well as FP2 and FP4. Stats was just reminding myself how to use the calculator correctly xD
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    (Original post by RDKGames)
    My retakes were Core 1 (orginally B), FP1 (originally B) and S1 (originally D) and this year I think they went far better so I can balance out my AS Further Maths at an A. My Loughborough offer is AAA for studying Mathematics but at this rate I should be getting A*A*B, if not Loughborough then I'm off to Leicester aha. I don't mind M3 as I'm doing an extra module which would replace it (which is D2) given that it goes better than M3, which most likely will lol but I still need to do good in it xD

    Also retakes are absolutely no pressure really, C1 and FP1 were naturally covered as I worked through C3 and C4 as well as FP2 and FP4. Stats was just reminding myself how to use the calculator correctly xD
    Np man, what do you want to do in university - if Maths then don't worry, you got a B but you're actually 2 grades higher lol. Also, universities will probably only care about Maths and FM if you want to do Maths and I'm thinking that the 2 A*s are in those two subjects, so don't worry :P. Oh lol and wow FP4 wtf lol that's some tough ass module probably.
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    (Original post by Chittesh14)
    Np man, what do you want to do in university - if Maths then don't worry, you got a B but you're actually 2 grades higher lol. Also, universities will probably only care about Maths and FM if you want to do Maths and I'm thinking that the 2 A*s are in those two subjects, so don't worry :P. Oh lol and wow FP4 wtf lol that's some tough ass module probably.
    Nah, the B is in FM probably, I'm just relying for some nice grade boundaries in August xD

    FP4 is decent; it deals with equations of planes, lines and their transformations using matrices all in 3 dimensional space. I enjoyed it as I'm good at visualising that stuff, but FM papers usually just throw one or two awkward questions which I get stuck on and lose some marks that lower my UMS lol, but these are the exact same questions I'm counting on to lower the grade boundaries.
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    (Original post by RDKGames)
    Nah, the B is in FM probably, I'm just relying for some nice grade boundaries in August xD

    FP4 is decent; it deals with equations of planes, lines and their transformations using matrices all in 3 dimensional space. I enjoyed it as I'm good at visualising that stuff, but FM papers usually just throw one or two awkward questions which I get stuck on and lose some marks that lower my UMS lol, but these are the exact same questions I'm counting on to lower the grade boundaries.
    Oh dam lol. I guess you took so hard modules lmao so they should be generous taking that into consideration. But, good luck anyway!
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    (Original post by SeanFM)
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    (Original post by RDKGames)
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    Hey guys.
    I was just wondering how I would approach and solve these questions.
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    8. Given that (x - 1) is a factor of 5x^3 - 9x^2 + 2x + a, find the value of a.

    9. Given that (x + 3) is a factor of 6x^3 - bx^2 + 18, find the value of b.

    10. Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7, find the value of p and q. [HINT: Solve simultaneous equations] ← ??

    I've actually solved them, but I don't even know how lol. I'll post my working out in a bit.
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    (Original post by Chittesh14)
    Hey guys.
    I was just wondering how I would approach and solve these questions.
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    8. Given that (x - 1) is a factor of 5x^3 - 9x^2 + 2x + a, find the value of a.

    9. Given that (x + 3) is a factor of 6x^3 - bx^2 + 18, find the value of b.

    10. Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7, find the value of p and q. [HINT: Solve simultaneous equations] ← ??

    I've actually solved them, but I don't even know how lol. I'll post my working out in a bit.
    These are very standard AS level questions - you should really have numerous examples in your textbook!

    If P(x) is a polynomial, then the statement "(x-1) is a factor of P(x)" means that we can write

    P(x) = (x-1)Q(x)

    where Q(x) is some other polynomial. So if we substitute x = 1 into both sides we get

    P(1) = 0(Q(1)) = 0

    i.e. if we substitute x = 1 into P(x) we get the answer 0. You questions 8, 9 and 10 are direct applications of this principle - for Q10 you just need to substitute in 2 values of x because you are given 2 linear factors and you have 2 unknowns to find.
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    (Original post by Chittesh14)
    Hey guys.I was just wondering how I would approach and solve these questions.
    Spoiler:
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    8. Given that (x - 1) is a factor of 5x^3 - 9x^2 + 2x + a, find the value of a.

    9. Given that (x + 3) is a factor of 6x^3 - bx^2 + 18, find the value of b.

    10. Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7, find the value of p and q. [HINT: Solve simultaneous equations] ← ??
    I've actually solved them, but I don't even know how lol. I'll post my working out in a bit.


    (Original post by davros)
    These are very standard AS level questions - you should really have numerous examples in your textbook!

    If P(x) is a polynomial, then the statement "(x-1) is a factor of P(x)" means that we can write

    P(x) = (x-1)Q(x)

    where Q(x) is some other polynomial. So if we substitute x = 1 into both sides we get

    P(1) = 0(Q(1)) = 0

    i.e. if we substitute x = 1 into P(x) we get the answer 0. You questions 8, 9 and 10 are direct applications of this principle - for Q10 you just need to substitute in 2 values of x because you are given 2 linear factors and you have 2 unknowns to find.
    Exactly what this guy said. Just sub in the values as you know they are factors of p(x)=0. Q10 should lead you to two equations with two unknowns hence the simultaneous equations.
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    (Original post by davros)
    These are very standard AS level questions - you should really have numerous examples in your textbook!

    If P(x) is a polynomial, then the statement "(x-1) is a factor of P(x)" means that we can write

    P(x) = (x-1)Q(x)

    where Q(x) is some other polynomial. So if we substitute x = 1 into both sides we get

    P(1) = 0(Q(1)) = 0

    i.e. if we substitute x = 1 into P(x) we get the answer 0. You questions 8, 9 and 10 are direct applications of this principle - for Q10 you just need to substitute in 2 values of x because you are given 2 linear factors and you have 2 unknowns to find.
    Sorry, I forgot about this question lol. Oh yeah, there is an example in the book (only 1) - I think I just missed it :/.
    Does my method work though lol somehow I got to a few answers, but it was very silly and too long compared to the textbook method.

    Thanks davros !
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    (Original post by RDKGames)
    Exactly what this guy said. Just sub in the values as you know they are factors of p(x)=0. Q10 should lead you to two equations with two unknowns hence the simultaneous equations.
    Yeah, worked it out a bit too late lol. 1 lesson learnt - look at the example in the textbook before coming to TSR!
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    (Original post by Chittesh14)
    Sorry, I forgot about this question lol. Oh yeah, there is an example in the book (only 1) - I think I just missed it :/.
    Does my method work though lol somehow I got to a few answers, but it was very silly and too long compared to the textbook method.

    Thanks davros !
    Is that a question mark in your working out for Q10? Lol restrain from using them, it's what we have letters for. :P
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    (Original post by RDKGames)
    Is that a question mark in your working out for Q10? Lol restrain from using them, it's what we have letters for. :P
    No, I was going to put a cross. But, I put a question mark to show confusion and so I remember to come back to it lol.
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    Find the real roots of the equation
     \displaystyle x^6+8x^5+16x^4+18x^3+16x^2+8x+1=  0 .
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    (Original post by Ano123)
    Find the real roots of the equation
     \displaystyle x^6+8x^5+16x^4+18x^3+16x^2+8x+1=  0 .
    I'm here to ask questions lol, not answer questions...... unless it relates to what I'm currently learning.
    Well, it might do so you're lucky - will attempt this one later.
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    (Original post by Chittesh14)
    I'm here to ask questions lol, not answer questions...... unless it relates to what I'm currently learning.
    Well, it might do so you're lucky - will attempt this one later.
    It's open for anyone to have a go at.
 
 
 
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