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
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Answers & Comments
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