Question

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

Answer 1

Answer:

-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