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Find all zeroes of x^3-2x

User Loesak
by
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2 Answers

5 votes

Answer:


\large\boxed{x=-\sqrt2,\ x=0,\ x=\sqrt2}

Explanation:


x^3-2x=0\qquad\text{distributive}\\\\x(x^2-2)=0\iff x=0\ \vee\ x^2-2=0\\\\x^2-2=0\qquad\text{add 2 to both sides}\\\\x^2=2\to x=\pm\sqrt2

User Tim Kruichkov
by
8.1k points
5 votes

You can factor out an x:

x (
x^(2) - 2)

Now set x equal to zero and the expression in the parentheses equal to zero

x = 0


x^(2)  - 2 = 0

We don't need to do anything to x = 0 because x is already isolated, but you can further isolate x in the equation:

x^2 - 2 = 0

To do this add 2 to both sides

x^2 = 2

Take the square root of both sides to completely isolate x

x = ± √2

The zeros are:

0 and ±√2

Hope this helped!

~Just a girl in love with Shawn Mendes

User Mcskinner
by
8.5k points

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