Question

find the value of 'a' for which the polynomial 4x⁴-ax³+2x²+4x+3 is divisible by (1-2x)​

Answer 1

Answer:

$Put 1-2x = 0 \\ x = \frac{1}{2} \\ since \: 1 - 2x \: divide \: the \: polynomial \: p(x) \\ therefore \: p( \frac{1}{2} ) = 0 \\ 4 \times {( \frac{1}{2}) }^{4} - a {( \frac{1}{2}) }^{3} + 2 {( \frac{1}{2} )}^{2} + 4 \times \frac{1}{2} + 3 = 0 \\ \frac{4}{16} - \frac{a}{8} + \frac{2}{4} + 2 + 3 = 0 \\ \frac{1}{4} - \frac{a}{8} + \frac{1}{2} + 5 = 0 \\ \frac{a}{8} = \frac{1}{4} + \frac{1}{2} + 5 \\ \frac{a}{8} = \frac{1 + 2 + 20}{4} \\ a = 46$