Question

The value of m if 2$y^3$ + m$y^2$ + 11y + m + 3 is exactly divisible by 2y - 1 is ________

• A. 7
• B. - 7
• C. - 1
• D. 1

Answer 1

The correct option is (D) - 7

Given, $2y^3+m\left(y^2\right)+11y+m+3$ is exactly divisible by $2y-1$

since 2y-1=0

$⟹$ 2y=1

$⟹$ y=$\frac{1}{2}$

Putting y= $\frac{1}{2}$ in 2$y^3$ + m$y^2$ + 11y + m + 3, we get

$\to 2{\left(\frac{1}{2}\right)}^3+m{\left(\frac{1}{2}\right)}^2+11\left(\frac{1}{2}\right)+m+3=0$

$\to$ $m=-7$

Hence, the value of m is -7.