Question 681095
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(x)=(x-5)(x-1)}}}
Then foil...or distribute...
{{{f(x)=x(x-1)-5(x-1)}}
{{{f(x)=x^2-x-5x+5}}}
{{{f(x)=x^2-6x+5}}}
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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<br>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^2+1}}}<br>
{{{f(x)=(x^2+1)(x^2-6x+5)}}}
{{{f(x)=x^2(x^2-6x+5)+1(x^2-6x+5)}}}
{{{f(x)=x^4-6x^3+5x^2+x^2-6x+5}}}
{{{f(x)=x^4-6x^3+6x^2-6x+5}}}

Hope that helped.  Happy Calculating!!!