Find the value of m so that 2 x-1 be a factor | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Let $p(x)=8 x^{4}+4 x^{3}-16 x^{2}+10 x+m.$

As $(2 x-1)$ is a factor of $p ( x )$

$	herefore \quad p\left(\frac{1}{2}ight)=0$ [By factor theo

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

Let $p(x)=8 x^{4}+4 x^{3}-16 x^{2}+10 x+m.$

As $(2 x-1)$ is a factor of $p ( x )$

$	herefore \quad p\left(\frac{1}{2}ight)=0$ [By factor theorem]

$\Rightarrow \quad 8\left(\frac{1}{2}ight)^{4}+4\left(\frac{1}{2}ight)^{3}-16\left(\frac{1}{2}ight)^{2}+10\left(\frac{1}{2}ight)+m=0$

$\Rightarrow \quad 8\left(\frac{1}{16}ight)+4\left(\frac{1}{8}ight)-16\left(\frac{1}{4}ight)+5+m=0$

$\Rightarrow \quad \frac{1}{2}+\frac{1}{2}-4+5+m=0$

$\Rightarrow \quad 2+m=0 \Rightarrow m=-2$

Find the value of $m$ so that $2 x-1$ be a factor of $8 x^{4}+4 x^{3}-16 x^{2}+10 x+m.$

Similar Questions

Factorise the following quadratic polynomials by splitting the middle term

$6 x^{2}+7 x-20$

Factorise

$16 x^{2}-16 x-21$

Expand

$(2 x-3)(2 x+5)$

Expand

$\left(\frac{x}{2}+\frac{2 y}{3}-\frac{3 z}{4}\right)^{2}$

Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by

$x-2$

Find the value of $m$ so that $2 x-1$ be a factor of $8 x^{4}+4 x^{3}-16 x^{2}+10 x+m.$

Similar Questions

Factorise the following quadratic polynomials by splitting the middle term $6 x^{2}+7 x-20$

Factorise $16 x^{2}-16 x-21$

Expand $(2 x-3)(2 x+5)$

Expand $\left(\frac{x}{2}+\frac{2 y}{3}-\frac{3 z}{4}\right)^{2}$

Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by $x-2$

Factorise the following quadratic polynomials by splitting the middle term

$6 x^{2}+7 x-20$

Factorise

$16 x^{2}-16 x-21$

Expand

$(2 x-3)(2 x+5)$

Expand

$\left(\frac{x}{2}+\frac{2 y}{3}-\frac{3 z}{4}\right)^{2}$

Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by

$x-2$