Question

Find a cubic polynomial whose zeros are 1/2, 1 ,and -3.

Answer 1

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Answer 2

Given that the zeros are 1/2, 1 and -3

⇒ The factors are (x - 1/2), (x - 1) and (x + 3)

Find the cubic polynomial:

(x - 1/2) (x - 1) (x + 3) = 0

(x - 1/2) (x ² + 3x - x - 3) = 0

(x - 1/2) (x² + 2x - 3) = 0

x³ + 2x² - 3x - 1/2x² - x + 3/2 = 0

x³ + 3/2x² - 4x + 3/2 = 0

2x³ + 3x² - 8x + 3 = 0

Answer: 2x³ + 3x² - 8x + 3 = 0