Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    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
    Name:  IMG_2059.jpg
Views: 91
Size:  487.9 KB
    Offline

    22
    ReputationRep:
    (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
    Name:  IMG_2059.jpg
Views: 91
Size:  487.9 KB
    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.
    Offline

    22
    ReputationRep:
    (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
    Name:  IMG_2059.jpg
Views: 91
Size:  487.9 KB
    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.
    Offline

    21
    ReputationRep:
    (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
    Name:  IMG_2059.jpg
Views: 91
Size:  487.9 KB
    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.
    Offline

    21
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (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
    Offline

    22
    ReputationRep:
    (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!
    Offline

    22
    ReputationRep:
    (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.
    Offline

    21
    ReputationRep:
    (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?
    Offline

    22
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (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
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brussels sprouts
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.