Question

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

Answer 1

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

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

$D=-16$

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

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

$D=-55$

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.