A polynomial in x whose zeros are -2, -1 and 3 is
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Correct Answer: Option D
Explanation:
x = -2, x = -1 and x = 3
∴x+2 = 0, x+1 = 0 and x-3 = 0
Product of the factors
(x+2)(x+1)(x-3) = 0
(x2 + 3x + 2)(x-3)
x(x2 + 3x + 2) -3(x2 + 3x + 2) = 0
x3 + 3x2 + 2x - 3x2 - 9x - 6 = 0
x3 - 7x - 6 = 0
x = -2, x = -1 and x = 3
∴x+2 = 0, x+1 = 0 and x-3 = 0
Product of the factors
(x+2)(x+1)(x-3) = 0
(x2 + 3x + 2)(x-3)
x(x2 + 3x + 2) -3(x2 + 3x + 2) = 0
x3 + 3x2 + 2x - 3x2 - 9x - 6 = 0
x3 - 7x - 6 = 0