15, Find a cubic polynomial whose zeroes are 3, and -12

1.	15, Find a cubic polynomial whose zeroes are 3, and -12
Answer» Given that the zeros are 3, 1/2 and -1 ⇒ The factors are (x - 3), (x - 1/2) and (x + 1) Find the cubic polynomial: (x - 3) (x - 1/2) (x + 1) = 0 (x - 3) (x ² + x - x/2 - 1/2) = 0 (x - 3) (2x² + x - 1) = 0 2x³ + x² - x - 6x² - 3x + 3 = 0 2x³ - 5x² - 4x + 3 = 0 Answer: 2x³ - 5x² - 4x + 3 = 0

Answer»

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

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

Find the cubic polynomial:

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

(x - 3) (x ² + x - x/2 - 1/2) = 0

(x - 3) (2x² + x - 1) = 0

2x³ + x² - x - 6x² - 3x + 3 = 0

2x³ - 5x² - 4x + 3 = 0

Answer: 2x³ - 5x² - 4x + 3 = 0

Discussion