Question

If AM and HM of the roots of a quadratic equation are 3/2 and 4/3 respectively, then that equation is.

• A. $x^2+3x+2=0$
• B. $x^2-3x+2=0$
• C. $x^2-3x-2=0$
• D. none of these

Answer 1

Answer: (B)

$x^2-3x+2=0$

Let $\alpha ,\beta$ are the roots
Given A.M is 3/2 $\Rightarrow \frac{\alpha +\beta }{2}=\frac{3}{2}\Rightarrow \alpha +\beta =3..\left(1\right)$
And H.M is 4/3 $\Rightarrow \frac{2\alpha .\beta }{\alpha +\beta }=\frac{4}{3}\Rightarrow \alpha .\beta =2$ using (1)
Hence required quadratic is, $x^2-(\alpha +\beta )x+\alpha .\beta =0\Rightarrow x^2-3x+2=0$