# If 2 and 0 are the zeros of the polynomial

Question:

If 2 and 0 are the zeros of the polynomial $f(x)=2 x^{3}-5 x^{2}+a x+b$ then find the values of $a$ and $b$.

Hint $f(2)=0$ and $f(0)=0$

Solution:

It is given that 2 and 0 are the zeroes of the polynomial $f(x)=2 x^{3}-5 x^{2}+a x+b$.

$\therefore f(2)=0$

$\Rightarrow 2 \times 2^{3}-5 \times 2^{2}+a \times 2+b=0$

$\Rightarrow 16-20+2 a+b=0$

$\Rightarrow-4+2 a+b=0$

$\Rightarrow 2 a+b=4$    .......(1)

Also,

$f(0)=0$

$\Rightarrow 2 \times 0^{3}-5 \times 0^{2}+a \times 0+b=0$

$\Rightarrow 0-0+0+b=0$

$\Rightarrow b=0$

Putting b = 0 in (1), we get

$2 a+0=4$

$\Rightarrow 2 a=4$

$\Rightarrow a=2$

Thus, the values of a and b are 2 and 0, respectively.