The quadratic equation whose roots are reciprocal of the roots of the equation `ax^(2) + bx+c=0` is :

Options

A. `abx^(2) + (b^(2)+ac) x + bc = 0`
B. `2abx^(2) + (b^(2) + 4ac) x + 2bc = 0`
C. `2ab x^(2) + (b^(2)+ac) x + bc = 0`
D. none of these

Answer

B

Explanation

Let `alpha, beta` be the roots of the given equation. Then, `alpha + beta = - b//a and alpha beta = c//a`
The A.M. and H.M. of `alpha and beta` are
`"A.M." = (alpha+beta)/(2) and "H.M." - (2alpha beta)/(alpha+beta)` respectively.
So, required equation is `x^(2)-x((alpha+beta)/(2)+(2alpha beta)/(alpha+beta))+((alpha+beta)/(2))((2alpha beta)/(alpha+beta))=0`
or, `2abx^(2) + (b^(2)+4ac) x + 2bc = 0`