Question

If p(x)=(x^4-x^2+x)then p(1/2) is
A 1/6
B 3/16
C 5/16
D 7/16

Answer 1

Answer:

$p(x) = {x}^{4} - {x}^{2} + x \\ \\ so \: \: \: p( \frac{1}{2} ) = {( \frac{1}{2}) }^{4} - {( \frac{1}{2} )}^{2} + \frac{1}{2} \\ \\ = \frac{1}{16} - \frac{1}{4} + \frac{1}{2} \\ \\ = \frac{1}{16} - \frac{1 \times 4}{4 \times 4} + \frac{1 \times 8}{2 \times 8} .........lcm \: \: \: \: of \: \: \: the \: \: \: denominator \\ \\ = \frac{1}{16} - \frac{4}{16} + \frac{8}{16} \\ \\ = \frac{1 - 4 + 8}{16} \\ \\ p( \frac{1}{2} ) \: \: \: = \: \: \: \frac{5}{16}$

OPTION ( C ) IS THE CORRECT ANSWER