Question

If x = 2 and x = 0 are roots of the polynomial f(x) = 2x3 – 5x2 + cx + d. Find the values of c and d.

Answer 1

f ( x ) = 2x³ – 5x² + cx + d

x = 2 is a root of f ( x )

implies

f ( 2 ) = 2 ( 2 )³ – 5 ( 2 )² + c ( 2 ) + d = 0

2 ( 8 ) – 5 ( 4 ) + 2c + d = 0

16 – 20 + 2c + d = 0

– 4 + 2c + d = 0

2c + d = 4. – ( 1 )

Also, x = 0 is a root of f ( x )

implies

f ( 0 ) = 2 ( 0 )³ – 5 ( 0 )² + c ( 0 ) + d = 0

0 – 0 + 0 + d = 0

d = 0

Put in eq ( 1 )

2c + 0 = 4

2c = 4

c = 4/2

c = 2