# Roots ><

• Oct 7th 2008, 04:34 AM
teddybear67
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.
• Oct 7th 2008, 05:17 AM
Plato
I am no fully clear as to what is required here. But this may help you.
The numbers a & b are roots of $(x-a)(x-b)=x^2 - (a+b) + ab = 0$.
• Oct 7th 2008, 05:19 AM
teddybear67
hey plato!
and erm,i dont really get what you mean by
$
(x-a)(x-b)=x^2 - (a+b) + ab = 0
$

sorry, my maths is really bad ><
• Oct 7th 2008, 08:49 AM
masters
Quote:

Originally Posted by teddybear67
hey plato!
$