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Find all the zeroes of the equation.
x4–6x2–7x–6=0
To find the zeroes of the equation x^4 - 6x^2 - 7x - 6 = 0, we can use factoring and the quadratic formula.
First, we can factor the equation by grouping:
x^4 - 6x^2 - 7x - 6 = 0
x^2(x^2 - 6) - 1(7x + 6) = 0
x^2(x^2 - 6) - 1(7x + 6) = 0
Now, we can factor the quadratic expression x^2 - 6:
x^2 - 6 = (x + √6)(x - √6)
Putting it all together:
(x^2 - 1)(x + √6)(x - √6) = 0
Setting each factor to 0, we get:
x^2 - 1 = 0
(x + 1)(x - 1) = 0
x = 1, -1
x + √6 = 0
x = -√6
x - √6 = 0
x = √6
Therefore, the zeroes of the equation x^4 - 6x^2 - 7x - 6 = 0 are x = 1, -1, √6, and -√6.