SOLUTION: What is a quartic function with only the two real zeroes given? x=5 and x=1

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Question 681095: What is a quartic function with only the two real zeroes given?
x=5 and x=1
Found 2 solutions by ReadingBoosters, funmath:
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
x-5=0 and x-1=0
(x-5)(x-1) =0
f(x) = x%5E2+-+6x+%2B+5
- Reading Boosters

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Question:What is a quartic function with only the two real zeroes given?
x=5 and x=1
I'm not sure you meant quartic. If you meant "quadratic" then you would merely solve it backwards. We usually factor and set each factor = to 0 and solve for x...so we will unsolve it...
x=5 and x=1
x-5=5-5 and x-1=1-1
x-5=0 and x-1=0
That reveals the factors before you solved.
f%28x%29=%28x-5%29%28x-1%29
Then foil...or distribute...
f%28x%29=x%28x-1%29-5%28x-1%29%7D%7D%0D%0A%7B%7B%7Bf%28x%29=x%5E2-x-5x%2B5
f%28x%29=x%5E2-6x%2B5
If you meant quadratic...you're done here.
*note* This is not the only answer that yields this result as you can multiply the function by any constant other than 0 and still get those results.
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If you meant quartic. Quartic is a function where the leading term has a forth power. So, you can multiply the quadratic function times any other quadratic function that only gives you complex answers...the easiest would be x%5E2%2B1

f%28x%29=%28x%5E2%2B1%29%28x%5E2-6x%2B5%29
f%28x%29=x%5E2%28x%5E2-6x%2B5%29%2B1%28x%5E2-6x%2B5%29
f%28x%29=x%5E4-6x%5E3%2B5x%5E2%2Bx%5E2-6x%2B5
f%28x%29=x%5E4-6x%5E3%2B6x%5E2-6x%2B5
Hope that helped. Happy Calculating!!!