# Precalculus

"Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation."

I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the imaginary roots. I checked HotMath but all it showed me was how to get the real roots and then it practically gave me the imaginary roots without showing how to work it out. Does anyone know how to do this? Any help is GREATLY appreciated!! :D

1. 👍 0
2. 👎 0
3. 👁 463
let y = x^3
y^2 - 7y - 8 = 0
(y-8)(y+1) = 0
so y = 8 or y = -1

then x^3 = 8 or x^3 = -1
x^3 - 8 = 0
(x-2)(x^2 + 2x + 4) = 0
this will give you the real root of x=2 and 2 imaginary roots from the quadratic

or
x^3 + 1 = 0
(x+1)(x^2 - x + 1) = 0
here x = -1 plus 2 more imaginary roots

1. 👍 0
2. 👎 0
2. Ohhhh duh!! I can't believe I totally overlooked that. Thanks Reiny!! :D

1. 👍 0
2. 👎 0

## Similar Questions

1. ### algebra 2

A quadratic equation can be written in vertex form or in standard form. Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why a.

2. ### Math

The graph of a quadratic function has vertex(3,-4) and passes through the point (4,1). Find the equation of the function in standard form. Rewrite the equation in general form. Could someone explain to me how to do this, just

3. ### math

which form of a quadratic funtion is easiest to use to find the maximum or minimum value of the function? satandard form factored form vertex form any form ***********

4. ### algebra 2

a quadratic equation can be written in vertex form or in standard form. sometimes one form is more beneficial than the other. identify which form would be more helpful if you needed to do each task listed below and explain why. a.

1. ### Algebra

For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work. y = -2x2 + 2x +2 -(1/2)y=x^2-x-1 (-1/2)y+1=x^2-x (-1/2)y+1=(x-1/2)^2-14 (-1/2)y=(x-1/2)^2-5/4

2. ### mathematic

. Form a quadratic equation in the form ax²+bx+c=0 whose roots are b and twice the negative reciprocal of b. (3mk)

3. ### math

Algebraically analyze the graph of the function f(x)= -6x^2+5x+2 . Find the vertex, axis of symmetry, range, minimum or maximum value, increasing and decreasing intervals, and zeros. Write the Quadratic equation in standard form.

4. ### maths

Form a quadratic equation in the form ax^2+bx+c=0 whose roots are b and twice the negative reciprocal of b.plz explain in detail

1. ### algebra

can someone explain the benefits of writing a quadratic equation in vertex form and benefits of writing a quadratic equation in standard form? Name specific methods you can use while working with one form or the other. Any help

2. ### algerba

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has? What are the solutions to the quadratic equation 4(x +

3. ### Algebra

1)Find the exact solutions to 3x^2=5x-1 using the quadratic formula. answer=5 plus or minus the square root of 37 over 6 2)Use the discriminant to determine the number and type of roots for the equation 2x^2-7x+9=0 answer=2

4. ### Math

a) Explain the relationship between the axis of symmetry and the quadratic formula. b) We know that the quadratic formula can be used to determine the roots of a quadratic function. However, the quadratic formula also reveals how