How do you find all zeros of the function #f(x)=8x^2+53x-21#?

1 Answer
George C.
May 30, 2016

#x=3/8# and #x=-7#

Explanation:

We can use an AC method to factor the quadratic.

Find a pair of factors of #AC=8*21 = 168# which differ by #53#.

The pair #56, 3# works in that #56*3 = 168# and #56-3 = 53#.

Use this pair to split the middle term and factor by grouping:

#8x^2+53x-21#

#=8x^2+56x-3x-21#

#=(8x^2+56x)-(3x+21)#

#=8x(x+7)-3(x+7)#

#=(8x-3)(x+7)#

Hence the zeros of #f(x)# are #x=3/8# and #x=-7#

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