# If b is the largest zero of x^{3}-5x^{2}-x+5 then which

If b is the largest zero of ${x}^{3}-5{x}^{2}-x+5$ then which of the following quadratic equations is it also a zero of?
1) ${x}^{2}-3x-10=0$
2) ${x}^{2}+3x-10=0$
3) ${x}^{2}-3x+10=0$
4) ${x}^{2}+3x+10=0$
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Utskoldendv3
First factor ${x}^{3}-5{x}^{2}-x+5$ by grouping to find its zeros:
${x}^{3}-5{x}^{2}-x+5$
$=\left({x}^{3}-5{x}^{2}\right)-\left(x-5\right)$
$={x}^{2}\left(x-5\right)-1\left(x-5\right)$
$=\left({x}^{2}-1\right)\left(x-5\right)$
$=\left(x-1\right)\left(x+1\right)\left(x-5\right)$
which has zeros: $1,-1.5$
So $b=5$
Substituting this value of b for x in 1), we find:
${x}^{2}-3x-10={5}^{2}-\left(3\cdot 5\right)-10=25-15-10=0$
So the answer 1) ${x}^{2}-3x-10=0$