Question

Find the value of $I$, so that $y-2p$ is a factor of $\frac{y^3}{4p^2}-2y+Ip$.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

To find the value of $I$, so that $y-2p$ is a factor of

$\frac{y^3}{4p^2}-2y+Ip$

Let, $f\left(y\right)=\frac{y^3}{4p^2}-2y+Ip$

Since, $y-2p$ is a factor of f(y)

i.e $y-2p=0$

$y=2p$

Therefore $f\left(2p\right)=0$

$\frac{(2p{)}^3}{4p^2}-2\left(2p\right)+Ip=0$

$\frac{8p^3}{4p^2}-4p+Ip=0$

$2p-4p+Ip=0$

$Ip-2p=0$

$Ip=2p$

$p(I-2)=0$

$I=2,p=0$

$I=2$

Hence , Option C