Question

find the value if p, if (2x+1) is a factor of 2x^3+px^3+11x+p+3
​

Answer 1

solution,

Given,

$p(x)=2x^3+px^2+11x+p+3$

$d(x)=2x+1$

now,

taking d(x),

d(x)= 2x+1

    =$2(x+\frac{1}{2})$

comparing$(x+\frac{1}{2})$ with (x-a), we get,

:. a=$-\frac{1}{2}$

Now,

As $(x+\frac{1}{2})$ is factor of p(x),

P(x)= p(a)= 0                                                   [As according to factor theorem]

or, $2x^3+px^2+11x+p+3=0$

or, $2(-\frac{1}{2})^3+p(-\frac{1}{2})^2+11(-\frac{1}{2})+p+3=0$

or, $-\frac{2}{8}+\frac{p}{4}-\frac{11}{2} +p+3=0$

or, $\frac{p}{4}+p-\frac{1}{4}-\frac{11}{2}+3=0$

or,$\frac{p+4p-1-22+12}{4}$=0

or, 5p-11=0

or, 5p=11

:. $p=\frac{11}{5}$