Question

If $x=2$ and $x=0$ are roots of the polynomials
$f\left(x\right)=2x^3-5x^2+ab+b$, then choose the correct options: -

• A. $a=2$
• B. $b=2$
• C. $a=0$
• D. $b=0$

Answer 1

Answer: (A), (D)

The correct options are
A $a=2$
D $b=0$

If $f\left(2\right)=2(2{)}^3-5(2{)}^2+a\left(2\right)+b=0$
$\Rightarrow 16-20+2a+b=0\Rightarrow 2a+b=4$
$\Rightarrow f\left(0\right)=2(0{)}^3-5(0{)}^2+a\left(0\right)+b=0$
$\Rightarrow b=0\Rightarrow 2a=4\Rightarrow a=2,b=0$