Find all the zeroes of the equation. x4 - 6x2 - 7x - 6 = 0

-2, 3, - 0.5 + 0.866i, - 0.5 - 0.866i.

Step-by-step explanation:

As the last term is - 6, + / - 2, + / - 3 are possible zeroes.

Try 2:-

(2) ^4 - 6 (2) ^2 - 7 (2) - 6 = - 28 so 2 is not a zero.

3:-

(3) ^4 - 6 (3) ^2 - 7 (3) - 6 = 0 so 3 is a zero.

(-2) ^4 - 6 (-2) ^2 - 7 (-2) - 6 = 0 so - 2 is also a zero.

Divide the function by (x + 2) (x - 3), that is x^2 - x - 6

gives x^2 + x + 1

x^2 + x + 1

So we have x^2 + x + 1 = 0

x = [-1 + / - √ (1^1 - 4*1*1) ] / 2

= - 1 + √ (-3) / 2, - 1 - √ (-3) / 2.

= - 0.5 + 0.866i, - 0.5 - 0.866i