Question

Choose the correct answer from the alternatives given :
When (x + 1) and (x - 2) are the factors of the expression $(2x^3-p{x}^2+x+q)$ then the values of p and q are given by

• A. $p=5,q=2$
• B. $p=7,q=8$
• C. $p=15,q=12$
• D. $p=7,q=10$

Answer 1

The correct option is D $p=7,q=10$

$\Rightarrow$ $(x+1)$ and $(x-2)$ are factors of the given equation $2x^3-p{x}^2+x+q=0$

Now substituting $x=-1$, in given equation

$\Rightarrow$ $2(-1{)}^3-p(-1{)}^2+(-1)+q=0$

$\Rightarrow$ $-2-p-1+q=0$

$\Rightarrow$ $-p+q-3=0$

$\therefore$ $-p+q=3$ ----- ( 1 )

Now, substituting $x=2$ we get,

$\Rightarrow$ $2(2{)}^3-p(2{)}^2+2+q=0$

$\Rightarrow$ $16-4p+2+q=0$

$\therefore$ $-4p+q=-18$ ------ ( 2 )

Now subtracting equation (2) from ( 1 ), we get

$\Rightarrow$ $3p=21$

$\therefore$ $p=7$

Now, substituting $p=7$ in equation ( 1 ),

$\Rightarrow$ $-\left(7\right)+q=3$

$\therefore$ $q=10$

$\therefore$ $p=7$ and $q=10$