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

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

To do: To find the value of $k$.

Solution:

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

Then, put $x=-3$ in the given polynomial and it must satisfy the polynomial.

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

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

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

$\Rightarrow 6k-8=0$

$\Rightarrow 6k=8$

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

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

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

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Updated on: 10-Oct-2022

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