Question

Question 1
If one of the zeroes of the quadratic polynomial $(k–1)x^2+kx+1$ is -3, then the value of k is
Thinking process
If $\alpha$ is the one of the zeroes of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+cthen,f\left(\alpha \right)$ must be equal to 0.
(A) 4/3
(B) –4/3
(C) 2/3
(D) –2/3

Answer 1

Given that, one of the zeroes of the quadratic polynomial say p(x) = (k – 1)x2 + kx + 1 is -3. then p( - 3)=0
$\Rightarrow$ $(k–1)(-3{)}^2+k(-3)+1=0$
$\Rightarrow$ $9(k–1)–3k+1=0$
$\Rightarrow$ $9k–9–3k+1=0$
$\Rightarrow$ $6k–8=0$
$\Rightarrow$ $k=\frac{4}{3}$