Question

If A.M. and H.M. of the roots of a quadratic equation are $8$ and $5$ respectively, then the equation is

• A. $x^2+16x-40=0$
• B. $x^2-16x-40=0$
• C. $x^2+16x+40=0$
• D. $x^2-16x+40=0$

Answer 1

The correct option is D $x^2-16x+40=0$

Let the required roots be $a$ and $b$
Now,
$\frac{a+b}{2}=8\Rightarrow a+b=16\cdots \left(1\right)$
$\frac{2ab}{a+b}=5$
Using equation $\left(1\right)$,
$\Rightarrow \frac{2ab}{16}=5\Rightarrow ab=40\cdots \left(2\right)$

Now,
Sum of roots $=16$,
Product of roots $=40$
Hence, the required quadratic equation is
$x^2-16x+40=0$