The quardatic Equation whose roots are the reciprocal of the roots of the equation _ - ?

ax^2 + bx + c = 0

1 Answer
Aug 3, 2018

The reqd. quadratic eqn.is :
cx^2+bx+a=0

Explanation:

Let alpha and beta be the roots of the quadratic eqn.

ax^2+bx+c=0

:.alpha+beta=-b/a and alpha*beta=c/a

The reciprocal of the roots of this eqn. are : 1/alpha and 1/beta

So, the quadratic eqn. whose roots are 1/alpha and 1/beta is :

x^2-(1/alpha+1/beta)x+1/alpha*1/beta=0

=>x^2-((alpha+beta)/(alpha*beta))x+1/(alpha*beta)=0

=>x^2-((-b/a)/(c/a))x+1/(c/a)=0

=>x^2+b/cx+a/c=0

=>cx^2+bx+a=0