Question 68

The value of k for which (x-2) is a factor of ($$x^{2}$$ - kx + 2) is :

Solution

If $$(x - a)$$ is a factor of $$f(x)$$, then $$f(a) = 0$$

Now, $$(x - 2)$$ is factor of $$f(x) = (x^{2} - kx + 2)$$

Thus, putting $$x = 2$$

=> $$f(2) = (2^2 - 2k + 2) = 0$$

=> $$-2k = 0 - 4 - 2 = -6$$

=> $$k = \frac{-6}{-2} = 3$$

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