Question

Find a quadratic equation with $\frac{1}{8}$ as the sum and 2 as product of its rootss.

• A. $8x^2+x+16=0$
• B. $8x^2-x+16=0$
• C. $8x^2-x-16=0$
• D. $8x^2+x-16=0$

Answer 1

The correct option is B $8x^2-x+16=0$

Let, $\alpha and\beta$ be roots.
Given: $\alpha +\beta =\frac{1}{8};\alpha \beta =2$
Therefore required quadratic equation is $x^2-(\alpha +\beta )x+\alpha \beta =0$.
Put the values
$x^2-\frac{1}{8}x+2=0$
$8x^2-x+16=0$

Therefore, $8x^2-x+16=0$ is a quadratic equation with $\frac{1}{8}$ as the sum and 2 as product of its roots.