Choose the correct answer from the given four options in the following questions:
If one of the zeroes of the quadratic polynomial \( (k-1) x^{2}+k x+1 \) is \( -3 \), then the value of \( k \) is
(A) \( \frac{4}{3} \)
(B) \( \frac{-4}{3} \)
(C) \( \frac{2}{3} \)
(D) \( \frac{-2}{3} \)

Given: 

One of the zeroes of the quadratic polynomial $( k-1)x^{2}+kx+1$ is $-3$

To do: 

We have o find the value of $k$.

Solution:

One of the zeroes of the quadratic polynomial $( k-1)x^{2}+kx+1$ is $-3$

Put $x=-3$ in the given polynomial and it must satisfy the polynomial.

$\Rightarrow ( k-1)( -3)^2+k( -3)+1=0$

$\Rightarrow ( k-1)9-3k+1=0$

$\Rightarrow 9k-9-3k+1=0$

$\Rightarrow 6k-8=0$

$\Rightarrow 6k=8$

$\Rightarrow k=\frac{8}{6}$

$\Rightarrow k=\frac{4}{3}$

Therefore, the value of $k$ is $\frac{4}{3}$.

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Updated on: 10-Oct-2022

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