If x = 0 and x = -1 are the roots of the polynomial f (x) = 2x3-3x2+ax+b, find the value of a and b.
we have,
f (x) = 2x3-3x2+ax+b
Put,
x = 0
f (0) = 2 (0)3 – 3 (0)2 + a (0) + b
= 0 – 0 + 0 + b
= b
x = -1
f (-1) = 2 (-1)3 – 3 (-1)2 + a (-1) + b
= -2 – 3 – a + b
= -5 – a + b
Since, x = 0 and x = -1 are roots of f (x)
f (0) = 0 and f (-1) = 0
b = 0 and -5 – a + b = 0
= a – b = -5
= a – 0 = -5
= a = -5
Therefore, a = -5 and b = 0