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 $x=6$

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