If x = 0 and x = -1 are the roots of the polynomial f (x) = 2x3 - 3x2

1.	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.
Answer» 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

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.

Answer»

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