2005
Mathematics
67ca00ce0c643c71d77dee1f
A polynomial in x whose zeros are -2, -1 and 3 is
A.
x3 - 7x + 6
B.
x3 + 7x - 6
C.
x3 + 7x + 6
D.
x3 - 7x - 6
Correct Answer: x3 - 7x - 6
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 = 0THIS WEEK's
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