Question

value of m when 2x3+mx2+11m+3 exactly divisible by2x-1

Answer 1

Step-by-step explanation:

$since \: the \: equation \: is \: exactly \: divisible \: by \: 2x - 1 \: so \: 2x - 1 \: is \: a \: factor \: of \: it. \\ therefore \: 2x - 1 = 0 \\ 2x = 1 \\ x= \frac{1}{2} \\ by \: putting \: the \: value \: of \: x \: in \: the \: equation \: we \: get \\ 2 {x}^{3} + m {x}^{2} + 11m + 3 = 0 \\ 2 \times { (\frac{1}{2} })^{3} \: + \: m \times \ { (\frac{1}{2} })^{2} \: + 11 \times ( \frac{1}{2} ) \: + 3 = 0\\ = \frac{2}{8} + \frac{m}{4} + \frac{11}{2} + 3 = 0 \\ = \frac{1}{4} + \frac{m}{4} + \frac{11}{2} + 3 = 0\\ = \frac{1 + m + (11 \times 2) + (3 \times 4)}{4} = 0 \: \: \: \: simplifying \: it \\ = \frac{1 + m + 22 + 12}{4} = 0 \\ = \frac{35 + m}{4} = 0 \\ = 35 + m = 0 \: \: \: by \: cross \: multiplication \\ m = - 35 \: \: ans$