How do you solve 3x^7 - 243x^3=0?

2 Answers
Dec 12, 2015

x=0,3

Explanation:

First thing you want to do is factor. You can factor out 3x^3

(3x^3)(x^4-81)=0

Now set both factors to zero

3x^3=0

x^3=0

root(3)(x^3)=root(3)0

x=0

x^4-81=0

x^4=81

root(4)(x^4)=root(4)81

x=3

Dec 12, 2015

x=0,+-3

Explanation:

Factor out a common 3x^3.

3x^3(x^4-81)=0

Recognize a difference of squares.

3x^3(x^2+9)(x^2-9)=0

Recognize another difference of squares.

3x^3(x^2+9)(x+3)(x-3)=0

Set each part equal to 0.

3x^3=0
x=0

x^2+9=0
x^2=-9
x=+-3i (NONREAL ANSWERS)

x+3=0
x=-3

x-3=0
x=3

Thus, x=0,+-3.

Look at a graph:

graph{3x^7-243x^3 [-12.73, 12.58, -6.17, 6.48]}

The x-intercepts (the roots) are when x=0,+-3.