Question 1
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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Solution

Given that, one of the zeroes of the quadratic polynomial say $p (x) = (k - 1) x^{2} + k x + 1, i s - 3. t h e n p (- 3) = 0$
$\Rightarrow$ $(k - 1) (- 3)^{2} + k (- 3) + 1 = 0$
$\Rightarrow$ $9 (k - 1) - 3 k + 1 = 0$
$\Rightarrow$ $9 k - 9 - 3 k + 1 = 0$
$\Rightarrow$ $6 k - 8 = 0$
$\Rightarrow$ $k = \frac{4}{3}$

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