Made a mistake when typing problem in, what are the x-intercepts of: 6x^3-9x-x^5?

Question

Sorry, the previous one i had a 5 as a coefficent for the the highest degree, that was wrong.

Answer 1

y-intercepts are always easy. Plug in x=0. The answer is 0.

for x-intercepts, factor and set equal to 0.

=-x(-6x² + 9 + x^4)
= -x((x²)² - 6(x²) + 9)
= -x((x²) - 3)²

So the x-intercepts are 0 and √3 and -√3

Answer 2

y=6x^3-9x-x^5
rearranged: y = -x^5+6x^3-9x

At x-intercept, y=0. So,

0=-x^5+6x^3-9x
In this form of the equation, the x intercept is 0.

You can also factor by first dividing both sides by x. This leaves:

0=-x^4+6x^2-9
Then reverse the signs so you have a positive in the first coefficient (for x^4).
0= x^4-6x^2+9 factor this equation.
0= (x^2 -3)(x^2- 3)

x^2-3 = 0
x^2=3
x= sqrt 3

The x-intercepts are 0 and sqrt 3.

Answer 3

0, sqrt(3), -sqrt(3)

sqrt = square root