Question 1075770
Rational coefficients and irrational roots means the irrational roots occur as conjugate pairs.
So,
{{{P(x)=a(x+3)(x-sqrt(7))(x+sqrt(7))(x-(1-sqrt(6)))(x-(1+sqrt(6)))}}}
{{{P(x)=a(x+3)(x^2-7)(x^2-2x-5)}}}
So then,
{{{P(-1)=a(-1+3)(1-7)(1+2-5)}}}
{{{8=a(2)(-6)(-2)}}}
{{{a=1/3}}}
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.
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{{{P(x)=((x+3)(x^2-7)(x^2-2x-5))/3}}}
{{{P(0)=((0+3)(0-7)(0-0-5))/3}}}
{{{P(0)=((3)(-7)(-5))/3}}}
{{{P(0)=35}}}