Question

For a quadratic polynomial $p\left(x\right)=k{x}^2-2x-3k$, if sum of zeroes are equal to the product of zeroes, then the value of $k$ is

• A. $\frac{2}{3}$
• B. $\frac{-2}{3}$
• C. $\frac{3}{4}$
• D. $\frac{-3}{4}$

Answer 1

The correct option is B $\frac{-2}{3}$

given polynomial = $k{x}^2-2x-3k$

if $a{x}^2+bx+c$ is a polynomial then its sum of roots is given by $\frac{-b}{a}$ and product of roots is given by $\frac{c}{a}$

$\therefore$ sum of roots of given polynomial $=\frac{-(-2)}{k}=\frac{2}{k}$

product of roots $=\frac{-3k}{k}=-3$

it is given that sum of roots $=$ product of roots

$\frac{2}{k}=-3$

$k=\frac{-2}{3}$