Question

if alpha and beta are the roots of equation ax²+bx+c=0 find the value of α+β/α²+β²

Answer 1

Answer:

α+β= -b/a

α.β= c/a

(α+β)²= α²+β²+2α.β

α²+β²= (α+β)²-2α.β

α²+β²= (-b/a)²-2.c/a

α²+β²= b²/a²-2.c/a

α²+β²= (b²-2ac)/a²

α+β/α²+β²= (-b/a)/(b²-2ac)/a²

α+β/α²+β²= -b/(b²-2ac). Ans.

Answer 2

Simply here, we can write

Now ,

Where ‘a' and ‘b' are the roots of the quadratic equation given above.

A²-B² = (A+B).(A-B)

We know sum of the roots that is -b/a

The difference of the roots are given by √D/a

Now put and get,

Generally you must remember that the difference of the roots of the quadratic equation is √D/a

Hopefully it's helpful.

Try figuring this question below.

If a and b are the roots of the quadratic equation:

Ax²+Bx+C=0

Then figure out the the quadratic equation whose roots are given by.

1/a² and 1/b²

………………………