Question

Find all the zeros of each equation 7x^2-144=-x^4

X^3-x^2+5x-5=0

Answer 1

1. 3, -3, 4i, -4i.

2. 1, √5i, - √5i.

Explanation:

1. 7x^2 - 144 = -x^4

x^4 + 7x^2 - 144 = 0

Let y = x^2, then we have:-

y^2 + 7y - 144 = 0

(y + 16)(x - 9) = 0

y = -16 or 9.

So x +/- √9 or +/- √-16

x = 3, -3, 4i, -4i (answer).

2. x^3-x^2+5x-5=0

f(1) = 1 - 1 + 5 - 5 = 0

Therefore x = 1 is a zero.

Therefore x - 1 is a factor of the function.

To find the other zeroes we divide the function by x - 1:-

x^2 + 5 <----- is the result.

--------------------------

x - 1 ) x^3 - x^2 + 5x - 5

x^3 - x^2

5x - 5

5x - 5.

So we have:-

x^2 + 5 = 0

x^2 = -5

x = +/- √5 i.