Question

The function $f\left(x\right)=x^3-6x^2+ax+b$ where a and b are constants is exactly divisible by (x - 3) and leaves a remainder of - 55 when divided by (x + 2) The value of a and b is _________

• A. $a=-10,b=3$
• B. $a=10,b=3$
• C. $a=10,b=-3$
• D. $a=-10,b=-3$

Answer 1

The correct option is C $a=10,b=-3$

Given,
$f\left(x\right)=x^3-6x^2+ax+b$
Since it is exactly divisible by $(x-3)$
$=>f\left(3\right)=0$
$=>3^3-6\times 3^2+3a+b=0$
$=>3a+b=27$ --- (1)
And since it leaves a
remainder of $-55$ when divided by $(x+2)$
$=>f(-2)=-55$
$=>{(-2)}^3-6\times {(-2)}^2-2x+b=0$
$=>-2a+b=-23$ --- (2)
Solving equations $\left(1\right),\left(2\right)$, we get $a=10,b=-3$