Question

If the roots of the quadratic equations. ${hx}^2+21x+10=0(b\ne 0)$ are in the ratio 2 : 5. Find the possible values of h.

Answer 1

$h{x}^2+21x+10=0$

Let the roots be $2p$ & $5p$,

$2p+5p=\frac{-21}{h}$ & $10p^2=\frac{10}{h}$

$\Rightarrow 7p=\frac{-21}{h}$ & $p^2=\frac{1}{h}$

$p=\frac{-3}{h}$

$\Rightarrow \frac{9}{h^2}=\frac{1}{h}$

$\Rightarrow h=9$.