# Thread: produce of eq with sor and por

1. ## produce of eq with sor and por

roots a/b, 1/ab

sor = a/b + 1/ab
= (a^2+1 )/ab

por = a/b X 1/ab
= a/ab^2
=1/b^2

form the eq with details pls.

(answer provided is abx^2 -a^2x +1 = 0)

2. I presume "sor" means "sum of roots" and "por" means "product of roots".

From that, I also presume that you are to create a quadratic equation which has roots as given.

Let $ax^2 + bx + c$ be a quadratic equation.

The sum of roots is $-b/a$ and the product of roots is $c/a$.

(This can be proved from forming the product and sum of the roots as given by the quadratic formula $x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}$ and simplifying the expression you get.)

So this gives you $x^2 - \left({\frac {a}{b} + \frac {1}{ab}}\right) + \frac {1}{b^2}$

But if you simplify this equation, you don't get what you've given as the answer.

$x = \frac {a^2 \pm \sqrt {\left({a^2}\right)^2 - 4ab}} {2ab}$

and that's nowhere near an equation giving the above as roots.

So there's either something wrong with the question or it's been copied down wrong.