Question

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

Answer 1

Step-by-step explanation:

We need to write the function that have two real number zeros by calculating the discriminant i.e. $b^2-4ac$.

We know that,

If D>0  the roots are real and unequal

If D= 0 roots are real and equal

If D< 0 roots are imaginary or not real and unequal

Function (1)

$f(x)=x^2 + 6x + 8\\\\D=6^2-4\times 1\times 8\\\\D=4$

D>0  the roots are real and unequal

Function (2)

$g(x)=x^2 + 4x + 8\\\\D=4^2-4\times 1\times 8\\\\D=-16$

D<0  the roots are real and unequal

Function (3)

$h(x)=x^2 -12x+32\\\\D=(-12)^2-4\times 1\times 32\\\\D=16$

D>0  the roots are real and unequal

Function (4)

$k(x)=x^2 +4x-1\\\\D=(4)^2-4\times 1\times (-1)\\\\D=20$

D>0  the roots are real and unequal

Function (5)

$p(x)=5x^2 +5x+4\\\\D=(5)^2-4\times 5\times 4\\\\D=-55$

D<0  the roots are real and unequal

Function (6)

$t(x)=x^2 -2x-15\\\\D=(-2)^2-4\times 1\times (-15)\\\\D=64$

D>0  the roots are real and unequal

(1),(3),(4) and (6) have two real number zeroes.