If b is the largest zero of x3−5x2−x+5 then which of the following quadratic equations is it also a zero of?

1) x2−3x−10=0
2) x2+3x−10=0
3) x2−3x+10=0
4) x2+3x+10=0

1 Answer
George C.
May 4, 2016

1) x2−3x−10=0

Explanation:

First factor x3−5x2−x+5 by grouping to find its zeros:

x3−5x2−x+5

=(x3−5x2)−(x−5)

=x2(x−5)−1(x−5)

=(x2−1)(x−5)

=(x−1)(x+1)(x−5)

which has zeros: 1, −1, 5

So b=5

Substituting this value of b for x in 1) we find:

x2−3x−10=52−(3⋅5)−10=25−15−10=0

So the answer is 1) x2−3x−10=0

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