Question

if x=0 and x= -1 are roots of the polynomial f(x)=2x^3 -3x^2+ax+b find the value of a and b

Answer 1

$f(x) = 2x {}^{3} - 3x {}^{2} + ax + b \\ f(0) = 2 \times 0 {}^{3} - 3 \times 0 {}^{2} + a \times 0 + b = 0 \\ 0 - 0 + 0 + b = 0 \\ b = 0$
$f( - 1) = 2 \times ( - 1) {}^{3} - 3 \times ( - 1) {}^{2} + a \times 1 + b = 0 \\ - 2 - 3 + a + 0 = 0 \\ - 5 + a = 0 \\ a = 5$
So, a=5
and b=0

Answer 2

I think it should be like this