作业帮solve the equation .
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solve the equation .
solve the equation 2x³-3x²-11x+6=0 given that -2 is a zero of f(x)=2x³-3x²-11x+6.
要翻译和解题过程
solve the equation 2x³-3x²-11x+6=0 given that -2 is a zero of f(x)=2x³-3x²-11x+6.
要翻译和解题过程
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2x³ - 3x² - 11x + 6 = 0
First find a root by inspection:
P(x) = 2x³ - 3x² - 11x + 6
P(-2) = -16 -12 + 22 + 6 = 0 so (x + 2) is a factor of P(x)
Then after doing synthetic division:
2x² - 7x + 3 is found as a quadratic factor of P(x)
Factoring the quadratic:
(2x - 1)(x - 3)
So (x + 2)(2x - 1)(x - 3) = 0
x + 2 = 0 or 2x - 1 = 0 or x - 3 = 0
x = -2 or x = 1/2 or x = 3
2x³ - 3x² - 11x + 6 = 0
First find a root by inspection:
P(x) = 2x³ - 3x² - 11x + 6
P(-2) = -16 -12 + 22 + 6 = 0 so (x + 2) is a factor of P(x)
Then after doing synthetic division:
2x² - 7x + 3 is found as a quadratic factor of P(x)
Factoring the quadratic:
(2x - 1)(x - 3)
So (x + 2)(2x - 1)(x - 3) = 0
x + 2 = 0 or 2x - 1 = 0 or x - 3 = 0
x = -2 or x = 1/2 or x = 3