If #b# is the largest zero of #x^3-5x^2-x+5# then which of the following quadratic equations is it also a zero of?

Question

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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Answer 1 · 2016-05-04T06:25:56

1) #x^2-3x-10=0#

First factor #x^3-5x^2-x+5# by grouping to find its zeros:

#x^3-5x^2-x+5#

#=(x^3-5x^2)-(x-5)#

#=x^2(x-5)-1(x-5)#

#=(x^2-1)(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:

#x^2-3x-10 = 5^2-(3*5)-10 = 25-15-10 = 0#

So the answer is 1) #x^2-3x-10=0#