Question

Determine which functions have two real number zeros by calculating the discriminant, b2 – 4ac. Check all that apply.

Answer 1

A, C, D, and F

Explanation:

Edge

Answer 2

Answer with Step-by-step explanation:

We are given that

Discriminant, D=
`b^2-4ac`

When
`D\geq 0`

Then, the function have two real zeroes.

1.
`f(x)=x^2+6x+8`

By comparing withe general quadratic equation

`ax^2+bx+c=0`

We get a=1,b=6,c=8

Using the discriminant formula

`D=(6)^2-4(1)(8)=36-32=4>0`

Hence, function have two real zeroes.

2.
`g(x)=x^2+4x+8`

`D=(4)^2-4(1)(8)=16-32`

`D=-16<0`

Hence, the function have no two real number zeroes.

3.
`h(x)=x^2-12x+32`

`D=(-12)^2-4(1)(32)=144-128=16`

`D>0`

Hence, function have two real zeroes.

4.
`k(x)=x^2+4x-1`

`D=(4)^2-4(1)(-1)=16+4=20`

`D>0`

Hence, function have two real zeroes.

5.
`p(x)=5x^2+5x+4`

`D=(5)^2-4(5)(4)=25-80`

`D=-55<0`

Hence, the function have no two real number zeroes.

6.
`r(x)=x^2-2x-15`

`D=(-2)^2-4(1)(-15)=4+60=64`

`D>0`

Hence, function have two real zeroes.