Question

The quadratic equation whose roots are the A.M. and H.M. between the roots of the equation, $2x^2-3x+5=0$ is

• A. $4x^2-25x+10=0$
• B. $12x^2-49x+30=0$
• C. $14x^2-12x+35=0$
• D. $2x^2+3x+5=0$

Answer 1

Answer: (B)

$12x^2-49x+30=0$

Let $\alpha ,\beta$ are roots of $2x^2-3x+5=0$
And roots of required equation are $r,s$
Then
$r=\frac{\beta +\alpha }{2}=\frac{\frac{3}{2}}{2}=\frac{3}{4}$
And $s=\frac{2\alpha \beta }{\beta +\alpha }=\frac{2\times \frac{5}{2}}{\frac{3}{2}}=\frac{10}{3}$
Hence equation is

$(x-\frac{3}{4})(x-\frac{10}{3})=0$

$\Rightarrow 12x^2-49x+30=0$