Question

If one zero of the quadratic polynomial $k{x}^2+3x+k$ is 2 then the value of k is

(a) $\frac{5}{6}$ (b) $\frac{-5}{6}$ (c) $\frac{6}{5}$ (d) $\frac{-6}{5}$

Answer 1

Let the given quadratic polynomial be

$p\left(x\right)=k{x}^2+3x+k$


Given one of the zero of the quadratic polynomial is 2.

Hence p(2) = 0

Put x = 2 in p(x), we get

$p\left(2\right)=k(2{)}^2+3(2)+k$

$\Rightarrow 0=4k+6+k$
$\Rightarrow 0=6+5k$
$\therefore k=\left(\frac{-6}{5}\right)$

(d) $\frac{-6}{5}$ is correct answer