How do you find all the zeros of #f(x)=2x^2-7x-30#?

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Answer 1 · 2016-06-24T22:22:35

Zeros: #x=-5/2# and #x=6#

#f(x) = 2x^2-7x-30#

Use an AC method:

Find a pair of factors of #AC=2*30 = 60# which differ by #B=7#.

The pair #12, 5# works.

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

#2x^2-7x-30#

#=2x^2-12x+5x-30#

#=(2x^2-12x)+(5x-30)#

#=2x(x-6)+5(x-6)#

#=(2x+5)(x-6)#

Hence zeros #x=-5/2# and #x=6#