solve the equation .

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

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我女朋友刚刚跟我说这是一元三次方程式,但她懒得算=( 而你的题目刚好是复古题,所以我在网路上帮你找到答案了

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

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