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    hello, any help with questions 10 and 11 would be greatly appreciated. I have already worked out that a=-7, but I'm unsure as to how to show the equation has only one real root, and, frankly, I am completely lost on how to start question 11. Thank you in advance for any help
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    (Original post by Imo_rai)
    hello, any help with questions 10 and 11 would be greatly appreciated. I have already worked out that a=-7, but I'm unsure as to how to show the equation has only one real root, and, frankly, I am completely lost on how to start question 11. Thank you in advance for any help
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    Factorise the quadratic into a linear factor and a quadratic factor, i.e: of the form (x-3)(ax^2 + bx + c) = 0, you know one solution is given by x=3 and the other two by ax^2 + bx + c = 0. So you want the latter term to have 0 solutions, what does the discriminant have to be for that to happen? Compute the discriminant and show that it is indeed that.
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    (Original post by Imo_rai)
    hello, any help with questions 10 and 11 would be greatly appreciated. I have already worked out that a=-7, but I'm unsure as to how to show the equation has only one real root, and, frankly, I am completely lost on how to start question 11. Thank you in advance for any help
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    Q11: Look for factors, try plugging in x=-1, 1, -2, 2, -3, 3 - etc... look for factors, factorise the equation as much as you can.

    Also compute \frac{dy}{dx}, which will get you a cubic, set this equal to zero - solve by factorising, try values, factorise, etc...

    Then find the coordinates of the stationary points and plot them on a graph making use of the fact that you've factorised y so you know where the roots are going to be, you know the stationary points as well, that should be all.
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    (Original post by Imo_rai)
    hello, any help with questions 10 and 11 would be greatly appreciated. I have already worked out that a=-7, but I'm unsure as to how to show the equation has only one real root, and, frankly, I am completely lost on how to start question 11. Thank you in advance for any help
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    ok For Question 10, (x-3) = 0 in other words x = 3
    Set the equation to zero, 4x^3 + ax^2 -13x + 6 = 0.
    Sub x = 3 into the equation above and move everything to the other side
    until you have a x^2 = constant. Divide the constant by x^2 where x = 3 and you should find the value of a.

    1 real root means b^2-4ac = 0.

    Q11) At a stationery point, dy/dx = 0 so differentiate the equation y = 2x^4-7x^2-6x and make it equal to zero. Rearrange dy/dx=0 to find the value of x sub that value of x back into the original equation y = 2x^4-7x^2-6x to find the coordinates (x,y). To find the nature of the stationery point, d^2y/dx^2 (double differentiate) the original equation y = 2x^4-7x^2-6x and sub the value of x in.

    If d^2y/dx^2 gives a number thats negative its a max, if it gives a positive number its a minimum. If its zero then resort to first principal differentiating where you change the value of x for which dy/dx=0.
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    (Original post by Zacken)
    Factorise the quadratic into a linear factor and a quadratic factor, i.e: of the form (x-3)(ax^2 + bx + c) = 0, you know one solution is given by x=3 and the other two by ax^2 + bx + c = 0. So you want the latter term to have 0 solutions, what does the discriminant have to be for that to happen? Compute the discriminant and show that it is indeed that.
    Beat me to it. Y u no use latex? :rofl:

    Is your IAL results day tomorrow? I saw you did a ton of exams in Jan = lots of results to collect tomorrow! :gasp:

    Are all your STEP papers in summer I.e June?

    I wish you all the best and hope you clutch up the grades.
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    (Original post by Zacken)
    Q11: Look for factors, try plugging in x=-1, 1, -2, 2, -3, 3 - etc... look for factors, factorise the equation as much as you can.

    Also compute \frac{dy}{dx}, which will get you a cubic, set this equal to zero - solve by factorising, try values, factorise, etc...

    Then find the coordinates of the stationary points and plot them on a graph making use of the fact that you've factorised y so you know where the roots are going to be, you know the stationary points as well, that should be all.
    thank you, this has really helped
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    (Original post by XxKingSniprxX)
    Beat me to it. Y u no use latex? :rofl:
    In bed + 1:30 a.m = LaTeX some other time pls. :rofl:

    Your post was more helpful though!

    Is your IAL results day tomorrow? I saw you did a ton of exams in Jan = lots of results to collect tomorrow! :gasp:
    It is, I'm not sure I'll be getting my results tomorrow itself because my centre is a bit useless.

    Are all your STEP papers in summer I.e June?
    Indeed.

    I wish you all the best and hope you clutch up the grades.
    Thank you very much!
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    (Original post by Imo_rai)
    thank you, this has really helped
    Quick trick that your teacher won't know!

    If you have a polynomial x^{\text{some power}} + \cdots + d, then if your polynomial has integer roots, you need only try values of x that divide d.

    i.e: If I have x^3 + x + 20, the only values of x that I need try are x = \pm 1, \pm 2,  \pm 4, \pm 5, \cdotsI don't need to bother myself with x = \pm 3 since that doesn't divide 20.
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    (Original post by Zacken)
    In bed + 1:30 a.m = LaTeX some other time pls. :rofl:

    Your post was more helpful though!

    It is, I'm not sure I'll be getting my results tomorrow itself because my centre is a bit useless.

    Indeed.

    Thank you very much!
    Ah, its only 9:32pm here (uk) and your +4 hours ahead of me.
    Try to get some early rest if you can big day tomorrow.

    My centre told me they are going to post my results home for August results day as I'm a private candidate but I told them directly I'm going to turn up and collect it as I've got adjustment etc to call up if things go good + saves a lot of stress. Is your centre doing the same or do they post it online on a website for you to see?
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    (Original post by XxKingSniprxX)
    Ah, its only 9:32pm here (uk) and your +4 hours ahead of me.
    Try to get some early rest if you can big day tomorrow.

    My centre told me they are going to post my results home for August results day as I'm a private candidate but I told them directly I'm going to turn up and collect it as I've got adjustment etc to call up if things go good + saves a lot of stress. Is your centre doing the same or do they post it online on a website for you to see?
    Neither I or they have any clue as to when or how I'll be getting my results... so extra stress yay.
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    (Original post by Zacken)
    Quick trick that your teacher won't know!

    If you have a polynomial x^{\text{some power}} + \cdots + d, then if your polynomial has integer roots, you need only try values of x that divide d.

    i.e: If I have x^3 + x + 20, the only values of x that I need try are x = \pm 1, \pm 2,  \pm 4, \pm 5, \cdotsI don't need to bother myself with x = \pm 3 since that doesn't divide 20.
    this is great, you're right my teacher mustn't know that! Thank you, that will save me a lot of time
 
 
 
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