The Best Answer for Find all the zeroes of the equation: x^4 – 6x^2 – 7x – 6 = 0?
Let f(x) = x^4 – 6x^2 – 7x – 6
Note factors of the constant term –6 are ±1, ±2, ±3 and ±6
f(−2) = 0 means x+2 is a factor of f(x)
f(3) = 0 means x−3 is a factor of f(x)
Do long division or synthetic division or by inspection
f(x) = (x+2)(x−3)(x²+x+1)
(x+2)(x−3)(x²+x+1) = 0
x = −2 or x = 3 or x²+x+1 = 0
Solving the quadratic equation, in addition to the 2 real solutions,
x = ½(−1 ± i√3).
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