If x = 0 and x = -1 are the roots of the polynomial f(x)

Solution:

We know that, $f(x)=2 x^{3}-3 x^{2}+a x+b$

Given, the values of x are 0 and -1

Substitute x = 0 in f(x)

$f(0)=2(0)^{3}-3(0)^{2}+a(0)+b$

= 0 - 0 + 0 + b

= b .... 1

Substitute x = (-1) in f(x)

$f(-1)=2(-1)^{3}-3(-1)^{2}+a(-1)+b$

= -2 - 3 - a + b

= – 5 - a + b ..... 2

We need to equate equations 1 and 2 to zero

b = 0 and – 5 – a + b = 0

since, the value of b is zero

substitute b = 0 in equation 2

⟹ – 5 – a = – b

⟹ – 5 – a = 0

a = – 5

the values of a and b are - 5 and 0 respectively