Question

Determine the value of k, if x – 1/2 is a factor of the polynomial p(x) = x^2 + kx – 3.

Answer 1

Answer:

$x - \frac{1}{2} = 0 \\ x = \frac{1}{2} \\ p(x) = {x}^{2} + kx - 3 \\ p( \frac{1}{2} ) = {( \frac{1}{2} )}^{2} + k (\frac{1}{2} ) - 3 = 0 \\ \frac{1}{4} + k( \frac{1}{2} ) - 3 = 0 \\ k (\frac{1}{2} ) = 3 - \frac{1} = = {4} \\ k( \frac{1}{2} ) = \frac{12 - 1}{4} \\ k = \frac{11}{4} \times \frac{2}{1} \\ k = \frac{22}{4} \\ k = \frac{11}{2}$

Step-by-step explanation:

we have taken LCM while we are subtracting by 4 and in last line we have find the smallest no. by dividing it by 2.

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