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Math Help - Roots ><

  1. #1
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    Roots ><

    hey, ive got a few Qs here. hope someone could help me with them =)

    1) The roots of the quadratic equation are 2x^2 - 3x +7 = 0 are  \alpha and \beta
    i) Find the quadratic equation in X whose roots are  \frac{\alpha}{\beta} and \frac{\beta}{\alpha}

    I dont need the answer to this, i just wanna know what they mean by quadratic equation in X?

    2) The roots of the quadratic equation 2x^2 - 6c + 5 = 0 are  \alpha and \beta.
    Find the quadratic equation with interger coefficients whose roots are \frac{2}{\alpha} and \frac{2}{\beta}

    I dont need the answer to this, i just wanna know what they mean by quadratic equation with integer coefficients?

    3) Given that  \alpha and \beta are the roots of the equation x^2 - 3x = 5, find the value of  \frac{1}{\alpha^2} + \frac{1}{\beta^2} and show that  \alpha^4 = 57\alpha + 70

    4) The roots of the equation x^2 - \sqrt{13x} + 1 = 0 are p and q, where p>q. Without using a calculator, express \frac{p}{q} in the form of  \frac{a - \sqrt{b}}{c}, where a,b and c are prime numbers.

    5) The roots of the equation x^2 + mx + n = 0 are \alpha and \beta, where m and n are real constants. Express the following expression in terms of m and n.
    if  \alpha = \beta - 1, show that  4n = m^2 -1

    Really hope someone could help me. my exam is tomorrow and i really wanna know the answers by today.
    Thanks in advance!!^^
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  2. #2
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    I am no fully clear as to what is required here. But this may help you.
    The numbers a & b are roots of (x-a)(x-b)=x^2 - (a+b) + ab = 0.
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  3. #3
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    hey plato!
    thanks for replying! ^^
    and erm,i dont really get what you mean by
    <br />
(x-a)(x-b)=x^2 - (a+b) + ab = 0<br />

    sorry, my maths is really bad ><
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by teddybear67 View Post
    hey plato!
    thanks for replying! ^^
    and erm,i dont really get what you mean by
    <br />
(x-a)(x-b)=x^2 - (a+b) + ab = 0<br />

    sorry, my maths is really bad ><
    What Plato is saying is: If a and b are roots (zeros) of the quadratic equation, then (x - a) and (x - b) are factors. Therefore,

    (x -a )(x - b) = 0
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