Question 376338
Recall that if p and q are solutions, then {{{x=p}}} or {{{x=q}}}



So in this case, this means that if {{{sqrt(5)}}} or {{{6*sqrt(5)}}} are solutions then {{{x=sqrt(5)}}} or {{{x=6*sqrt(5)}}}



{{{x=sqrt(5)}}} or {{{x=6*sqrt(5)}}} Start with the given solutions.



{{{x-sqrt(5)=0}}} or {{{x-6*sqrt(5)=0}}} Get everything to the left side.



{{{(x-sqrt(5))(x-6*sqrt(5))=0}}} Use the zero product property



{{{x^2-6*sqrt(5)*x-sqrt(5)*x-sqrt(5)(-6*sqrt(5))=0}}} FOIL



{{{x^2-7*sqrt(5)*x+30=0}}} Multiply and combine like terms.



So the quadratic expression is {{{x^2-7*sqrt(5)*x+30}}}



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