Q70 / 180 · KCET 2024 · Mathematics
If $A M$ and $G M$ of roots of a quadratic equation are 5 and 4 , respectively, then the quadratic equation is
- A$x^2-10 x-16=0$
- B$x^2+10 x+16=0$
- C$x^2+10 x-16=0$
- Correct answerD$x^2-10 x+16=0$
Solution
Let $a$ and $b$ be the roots the quadratic equation.
Then, the quadratic equation is
$x^2-(a+b) x+a b=0$ ....(i)
It is given that $\mathrm{AM}=5$ and $\mathrm{GM}=4$
i.e. $\frac{a+b}{2}=5$ and $\sqrt{a b}=4$
$\Rightarrow a+b=10$ and $a b=16$
On substituting these values in Eq. (i), we obtain. Hence, $x^2-10 x+16=0$ is the required equation.
Hence, the correct answer is option: 'D'.