# Quadratic Equation

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• November 29th 2010, 03:47 AM
maskov
Quadratic Equation
Hi
Can anyone plz. point out is there anything wrong with the question given below ?
if its correct thrn how the solution will have to derived ?

Question
If α and β are the roots of the equation ax² + bx + c = 0 then Prove that
a² – 3b² – 2ab + 16ac = 0
• November 29th 2010, 05:10 AM
Sudharaka
Quote:

Originally Posted by maskov
Hi
Can anyone plz. point out is there anything wrong with the question given below ?
if its correct thrn how the solution will have to derived ?

Question
If α and β are the roots of the equation ax² + bx + c = 0 then Prove that
a² – 3b² – 2ab + 16ac = 0

Dear maskov,

You should know that,

$\alpha+\beta=-\dfrac{b}{a}$

$\alpha\beta=\dfrac{c}{a}$

Also, $a^{2}- 3b^{2} - 2ab +16ac = 0$

$\Rightarrow 1-3\left(\dfrac{b}{a}\right)^2-2\dfrac{b}{a}+16\dfrac{c}{a}=0$

Substitute for $\dfrac{b}{a} ~and~\dfrac{c}{a}$ and see whether the left and right hand sides are equal.
• November 29th 2010, 10:22 PM
maskov
Hi
Sudharaka
Thanks for your reply, substituting values of α + β and αβ does not make it zero.

Maskov
• November 30th 2010, 10:46 AM
Archie Meade
Quote:

Originally Posted by maskov
Hi
Can anyone plz. point out is there anything wrong with the question given below ?
if its correct thrn how the solution will have to derived ?

Question
If α and β are the roots of the equation ax² + bx + c = 0 then Prove that
a² – 3b² – 2ab + 16ac = 0

Do you have some condition relating the roots to each other ?
Numerous combinations of a, b, c will not satisfy the 2nd equation,
hence the roots ought to have a certain relationship.