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!!!!

Algebra ->  Quadratic Equations and Parabolas -> 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!!!!      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
a)

2x%5E2=6 Start with the given equation


x%5E2=3 Divide both sides by 2


x=sqrt%283%29 or x=-sqrt%283%29 Take the square root of both sides.


So the solutions are x=sqrt%283%29 or x=-sqrt%283%29


which approximate to x=1.732 or x=-1.732


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b)

f%28x%29=2x%5E2-6 Start with the given function


0=2x%5E2-6 Plug in f%28x%29=0


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=0, and c=-6


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%282%29%28-6%29+%29%29%2F%282%282%29%29 Plug in a=2, b=0, and c=-6


x+=+%28-0+%2B-+sqrt%28+0-4%282%29%28-6%29+%29%29%2F%282%282%29%29 Square 0 to get 0.


x+=+%28-0+%2B-+sqrt%28+0--48+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-6%29 to get -48


x+=+%28-0+%2B-+sqrt%28+0%2B48+%29%29%2F%282%282%29%29 Rewrite sqrt%280--48%29 as sqrt%280%2B48%29


x+=+%28-0+%2B-+sqrt%28+48+%29%29%2F%282%282%29%29 Add 0 to 48 to get 48


x+=+%28-0+%2B-+sqrt%28+48+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-0+%2B-+4%2Asqrt%283%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-0%29%2F%284%29+%2B-+%284%2Asqrt%283%29%29%2F%284%29 Break up the fraction.


x+=+0+%2B-+sqrt%283%29 Reduce.


x+=+sqrt%283%29 or x+=+-sqrt%283%29 Break up the "plus/minus" to form two equations.


So the answers are x+=+sqrt%283%29 or x+=+-sqrt%283%29


which approximate to x=1.732 or x=-1.732


So this means that the x-intercepts are and

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


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