Question

If (x+2) and (x-1) are factors of $x^3-(a+1)x^2-(b+2)x+10=0$, find the values of a and b

• A. a = 4, b= 9
• B. a = 3, b = 5
• C. a = 4, b= 5
• D. a = 8, b= 4

Answer 1

The correct option is B

a = 3, b = 5

Since (x + 2) is a factor of $x^3-(a+1)x^2-(b+2)x+10=0$, $\Rightarrow f(-2)=0$
$\Rightarrow (-2{)}^3-(a+1\left)\right(-2{)}^2-(b+2)(-2)+10=0$
$\Rightarrow -8-4(a+1)+2b+4+10=0$
$\Rightarrow -8-4a-4+2b+14=0$
$\Rightarrow -4a+2b+2=0$ ................(i)

Since (x-1) is a factor of $x^3-(a+1)x^2-(b+2)x+10=0$, $\Rightarrow f\left(1\right)=0$
$\Rightarrow (1{)}^3-(a+1\left)\right(1{)}^2-(b+2)1+10=0$
$\Rightarrow 1-a-1-b-2+10=0$
$\Rightarrow -a-b+8=0$...................(ii)

Solving Equation (i) and equation (ii), we get a = 3 and b = 5.