Question

If $x=2$, $x=0$ are roots of the polynomials $f\left(x\right)=2x^3-5x^2+ax+b$, then find the values of $a$ and $b$.

• A. $a=2,b=0$
• B. $a=7,b=0$
• C. $a=3,b=0$
• D. $a=1,b=0$

Answer 1

The correct option is A $a=2,b=0$

Given, $f\left(x\right)=2x^3-5x^2+ax+b$

Therefore, $f\left(2\right)=2(2{)}^3-5(2{)}^2+a\left(2\right)+b=0$

$\Rightarrow 16-20+2a+b=0\Rightarrow 2a+b=4$ ........... (i)

and $f\left(0\right)=2(0{)}^3-5(0{)}^2+a\left(0\right)+b=0$

$\Rightarrow b=0$

$\Rightarrow 2a=4$

$\Rightarrow a=2,b=0$