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

Question

asked Sep 20, 2021 113k views

2 Answers

Nightmare Games · Answer 1 · 2021-09-24T06:36:29+0000

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.