SOLUTION: Find all real zeros of the function: * f(x)=-7x^4+343x^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all real zeros of the function: * f(x)=-7x^4+343x^2      Log On


   

Question 90670: Find all real zeros of the function:
* f(x)=-7x^4+343x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-7x%5E4%2B343x%5E2=0 Set the expression equal to zero

-7x%5E2%28x%5E2-49%29=0 Factor out the GCF -7x%5E2

-7x%5E2%28x-7%29%28x%2B7%29=0 Factor the expression x%5E2-49 (note: if you need help with factoring, check out this solver)


Now set each factor equal to zero:

-7x%5E2=0, x-7=0 or x%2B7=0

x=0, x=7 or x=-7 Now solve for x in each case


So our solutions are x=0, x=7 or x=-7


Notice if we graph y=-7x%5E4%2B343x%5E2 we get

+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+-7x%5E4%2B343x%5E2%29+

and we can see that the graph has roots at x=0 (it's a little difficult to see this one), x=7 and x=-7, so this verifies our answer.