Question

Find the smallest zero for the function h(x) = 4x^2 - 8x - 60

Answer 1

Answer:

The smallest zero is x = -3

Step-by-step explanation:

We have been given the equation $h(x)=4x^2-8x-60$

In order to find the zero, h(x) = 0

$4x^2-8x-60=0$

We can rewrite the equation by factor out 4

$x^2-2x-15=0$

Middle term can be written as -2x = -5x+3x

$x^2-5x+3x-15=0$

Now, we factored out GCF

$x(x-5)+3(x-5)=0$

Factored out the common term

$(x-5)(x+3)=0$

Apply the zero product property

$(x-5)=0, (x+3)=0\\\\x=5,-3$

Hence, the smallest zero is x = -3

Answer 2

Note that h(x) = 4x^2 - 8x - 60 factors to 4(x^2 - 2x - 15), and that the roots (zeros) of (x^2 - 2x - 15) are -5 and +3.  Thus, the smallest zero is -5.