How can I graph this quadratic function?

[abel muroi]

I was asked to find the roots ( x-intercept) of this equation. I was also asked to graph the equation

R(x) = -x⁵ +5x³ - 4x

I know this is a fifth degree polynomial but I am having some difficulty trying to find the roots here.

Am I supposed to factor this?

anyway, here is my work


R(x) = -x⁵ +5x³ - 4x
R(x) = -x(x⁴ + 5x² - 4)

how do i find the roots here?

 

[Ishuda]

I was asked to find the roots ( x-intercept) of this equation. I was also asked to graph the equation

R(x) = -x⁵ +5x³ - 4x

I know this is a fifth degree polynomial but I am having some difficulty trying to find the roots here.

Am I supposed to factor this?

anyway, here is my work


R(x) = -x⁵ +5x³ - 4x
R(x) = -x(x⁴ + 5x² - 4)

how do i find the roots here?

Well, first you have a root at zero with that -x out front. BTW, you need to take the minus sign out also so that
R(x) = -x (x⁴ - 5 x² + 4).

To solve the 4th degree equation, try letting u = x² and solve the quadratic euation for u. If there is a positive u, take \(\displaystyle \pm\) of that to get the roots for x.

 

[abel muroi]

Well, first you have a root at zero with that -x out front. BTW, you need to take the minus sign out also so that
R(x) = -x (x⁴ - 5 x² + 4).

To solve the 4th degree equation, try letting u = x² and solve the quadratic euation for u. If there is a positive u, take \(\displaystyle \pm\) of that to get the roots for x.

ok so here is what i have so far..

-x (x⁴ - 5x² + 4).
-x (x² - 4)(x² - 1)
-x (x - 2)(x + 2)(x - 1)(x + 1)

so are these the roots x = 0, x = 2, x = -2, x = 1, x = -1?

 

[Ishuda]

ok so here is what i have so far..

-x (x⁴ - 5x² + 4).
-x (x² - 4)(x² - 1)
-x (x - 2)(x + 2)(x - 1)(x + 1)

so are these the roots x = 0, x = 2, x = -2, x = 1, x = -1?

Looks good to me. Glad to help but you can check them your self maybe faster by plugging the values back into the original equation or the one with the factored out (-x), i.e.
2⁴ - 5 2² + 4 = 16 - 20 + 4 = 0

 

[Steven G]

ok so here is what i have so far..

-x (x⁴ - 5x² + 4).
-x (x² - 4)(x² - 1)
-x (x - 2)(x + 2)(x - 1)(x + 1)

so are these the roots x = 0, x = 2, x = -2, x = 1, x = -1?

Now you need to decide how to graph it. There are many ways to figure out how to graph it. I like to figure out what the sign is if x is large. Well what does large mean? It means larger than ALL the roots. Please show us your graph.