Question

If one of the zeroes of the quadratic polynomial $(k-1)x^2+kx+1$ is $-3$, then the value of $k$ is.

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

Answer 1

The correct option is A $\frac{4}{3}$

Given $-3$ is the zero of the polynomial $(k-1)x^2+kx+1$

So $-3$ must satisfy the equation $(k-1)x^2+kx+1=0$

$⟹(k-1)(-3{)}^2+k(-3)+1=0$
$⟹9(k-1)-3k+1=0$

$⟹9k-9-3k+1=0$

$⟹6k=8$

$⟹k=\frac{4}{3}$