Question

How to find roots when the quadratic equation are reciprocal of each other

Answer 1

Answer:

Step-by-step explanation:

What happens if the roots of a quadratic equation are reciprocal of the roots of another quadratic eqUATION

Yeah I know, you wanted to know the relation between the coefficients of the two quadratic equations….

Let us take a quadratic equation ax2+bx+c=0. Let its roots be α,β.

We have α+β=−ba and αβ=ca.

Let us call the above as fact(1)

We want a quadratic equation with reciprocal roots, i.e. 1α,1β.

To form that quadratic equation let us find the sum and product of the ‘new’ roots using fact(1) :

1α+1β=α+βαβ=−bc

Likewise

1α∗1β=1αβ=ac

Now to write the required quadratic equation using

x2− (sum of roots)x+ (product of roots) = 0

x2+bcx+ac=0

Rearranging we get cx2+bx+a=0.

If ax2+bx+c=0, has roots α,β, then cx2+bx+a=0 will have roots 1α,1β.

The coefficient of x2 and the constant term are interchanged, but the coefficient of x remains the same.

Hope that was helpful,

Cheers