If -1 and-2 are the zeroes of the cubic polynomial x³-2x²+ax+b, then find the value of a and b

a = - 13, b = - 10

Step-by-step explanation:

Given that x = - 1 and x = - 2 are zeros then

f(- 1) = 0 and f(- 2) = 0, that is substituting value into the polynomial

f(- 1) = (- 1)³ - 2(- 1)² - a + b = 0 , that is

- 1 - 2 - a + b = 0

- a + b = 3 → (1)

f(- 2) = (- 2)³ - 2(- 2)² - 2a + b = 0, that is

- 8 - 8 - 2a + b = 0

- 2a + b = 16 → (2)

Multiply (1) by - 2

2a - 2b = - 6 → (3)

Add (2) and (3) term by term to eliminate a

- b = 10 ( multiply both sides by - 1 )

b = - 10

Substitute b = - 10 into (1) and evaluate for a

- a - 10 = 3 ( add 10 to both sides )

- a = 13 ( multiply both sides by - 1 )

a = - 13

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