SOLUTION: a)SOLVE 2X^2=6 b) Find the x-intercepts of f(x)=2x^2-6 What are the solutions? What are the x-intercepts? Thank you for any help!!!!

Question 155616: a)SOLVE 2X^2=6
b) Find the x-intercepts of f(x)=2x^2-6
What are the solutions?
What are the x-intercepts?

Thank you for any help!!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

Start with the given equation

Divide both sides by 2

or Take the square root of both sides.

So the solutions are or

which approximate to or

==================================================

b)

Start with the given function

Plug in

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the "plus/minus" to form two equations.

So the answers are or

which approximate to or

So this means that the x-intercepts are

and

which in decimal form are (1.732,0) and (-1.732,0)

======================================================

Notice how the solutions of the first equation are simply the x-coordinates of the x-intercepts.
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