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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