Question

Find the zeros of the function algebraically.f(x) = 4x2 + 9x − 28.
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start with 
(2x-    ) (x+   )

Answer 1

4x^2 +16x-7x-28=0
orr 4x(x+4)-7(x+4)
or   (4x-7)(x+4)=0
hence x=-4,7/4

Answer 2

$f(x)=4x^2+9x-28\\\\zeros\ if\ f(x)=0\Rightarrow4x^2+9x-28=0\\\\-28=4\times(-7)\\9x=16x-7x\\\\4x^2+16x-7x-7\times4=4x(x+4)-7(x+4)=(x+4)(4x-7)\\\\f(x)=0\iff(x+4)(4x-7)=0\iff x+4=0\ or\ 4x-7=0\\\\x=-4\ or\ 4x=7\\\\\boxed{x=-4\ or\ x=\frac{7}{4}}$