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2. Polynomials
medium
Find the value of $k$, if $x -1$ is a factor of $p(x)$ in this case : $p(x)=k x^{2}-3 x+k$
A
$\frac{2}{3}$
B
$-\frac{3}{2}$
C
$\frac{3}{2}$
D
$-\frac{2}{3}$
Solution
Here $\quad p ( x )= kx ^{2}-3 x + k$ and $g ( x )= x -1$
For $g(x)$ be a factor of $p(x), p(1)$ should be equal to $0 .$
since $\quad p (1)= k (1)^{2}-3(1)+ k = k -3+ k =2 k -3$
$\therefore$ $2 k-3=0 \quad \Rightarrow k=\frac{3}{2}$
Standard 9
Mathematics
