Question

if x=2 and x=0 are zeroes of the polynomial given below, find the values of a and b f(x) =2x^3 -5x^2 +ax+b

Answer 1

Answer:

a = 2

b = 0

Step-by-step explanation:

f(x) = 2x^3 - 5x^2 + ax +b

When x = 2,

= 2(2)^3 - 5(2)^2 + a(2) + b

= 2(8) - 5(4) +2a + b

= 16 - 20 + 2a + b

= 2a +b - 4 --------(1)

When x = 0,

= 2(0)^2 - 5(0)^2 + a(0) + b

= 0 - 0 + 0 + b

= b ----------(2)

From equation (1) & (2),

2a + b = 4

- b

----------------

2a = 4

a = 2

Similarly,

2a + b = 4

2(2) + b = 4

4 + b = 4

b = 4 - 4

b = 0