Determine which functions have two real number zeros by calculating the discriminant, b2 – 4ac. Check all that apply.
f(x) = x2 + 6x + 8
g(x) = x2 + 4x + 8
h(x) = x2 – 12x + 32
k(x) = x2 + 4x – 1
p(x) = 5x2 + 5x + 4
t(x) = x2 – 2x – 15

Question

vandervort.everardo · Accepted Answer

Step-by-step explanation:We need to write the function that have two real number zeros by calculating the discriminant i.e. [tex]b^2-4ac[/tex].We know that,If D&gt;0 the roots are real and unequalIf D= 0 roots are real and equalIf D&lt; 0 roots are imaginary or not real and unequalFunction (1)[tex]f(x)=x^2 + 6x + 8\\D=6^2-4	imes 1	imes 8\\D=4[/tex]D&gt;0 the roots are real and unequalFunction (2)[tex]g(x)=x^2 + 4x + 8\\D=4^2-4	imes 1	imes 8\\D=-16[/tex]D&lt;0 the roots are real and unequalFunction (3)[tex]h(x)=x^2 -12x+32\\D=(-12)^2-4	imes 1	imes 32\\D=16[/tex]D&gt;0 the roots are real and unequalFunction (4) [tex]k(x)=x^2 +4x-1\\D=(4)^2-4	imes 1	imes (-1)\\D=20[/tex]D&gt;0 the roots are real and unequalFunction (5) [tex]p(x)=5x^2 +5x+4\\D=(5)^2-4	imes 5	imes 4\\D=-55[/tex]D&lt;0 the roots are real and unequalFunction (6) [tex]t(x)=x^2 -2x-15\\D=(-2)^2-4	imes 1	imes (-15)\\D=64[/tex]D&gt;0 the roots are real and unequal(1),(3),(4) and (6) have two real number zeroes.