# 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) $\frac{-2}{3}$

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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 $\frac{4}{3}$.

Updated on 10-Oct-2022 13:27:08