Question 375885
If {{{x=i}}} is a solution, then so is {{{x=-i}}} since complex solutions only come in complex conjuate pairs.
{{{f(x)=a(x-1)(x-4)(x-i)(x+i)}}}
{{{f(x)=a(x-1)(x-4)(x^2+1)}}}
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{{{f(2)=a(2-1)(2-4)(2^2+1)=30}}}
{{{a(1)(-2)(5)=30}}}
{{{a=-3}}}
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{{{highlight(f(x)=-3(x-1)(x-4)(x^2+1))}}}