Question

If the roots of ax2+bx+c =0 are in the ratio p/q then the value of b^2/ca

Answer 1

Answer:

$\frac{b^2}{ca}=\frac{(p+q)^2}{pq}$

Step-by-step explanation:

Let the roots be $\alpha\:and\:\beta$

Given:

$\alpha:\beta=p:q$

$\alpha=kp\:and\beta=kq$

$\text{Sum of the roots}=\frac{-b}{a}$

$\frac{-b}{a}=kp+kq$

$\implies\frac{b}{a}=-k(p+q)$....(1)

$\text{Product of the roots}=\frac{c}{a}$

$\frac{c}{a}=kp.kq$

$\implies\frac{c}{a}=k^2pq$....(2)

Now,

$\frac{(1)^2}{(2)}$

$\frac{\frac{b^2}{a^2}}{\frac{c}{a}}=\frac{k^2(p+q)^2}{k^2pq}$

$\frac{b^2}{a^2}\times\frac{a}{c}=\frac{(p+q)^2}{pq}$

$\implies\boxed{\frac{b^2}{ca}=\frac{(p+q)^2}{pq}}$

Answer 2

Step-by-step explanation:

the another simplest method is given in the pic

If their is any doubt then ask in comment