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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

Respuesta :

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>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)

[tex]f(x)=x^2 + 6x + 8\\\\D=6^2-4\times 1\times 8\\\\D=4[/tex]

D>0  the roots are real and unequal

Function (2)

[tex]g(x)=x^2 + 4x + 8\\\\D=4^2-4\times 1\times 8\\\\D=-16[/tex]

D<0  the roots are real and unequal

Function (3)

[tex]h(x)=x^2 -12x+32\\\\D=(-12)^2-4\times 1\times 32\\\\D=16[/tex]

D>0  the roots are real and unequal

Function (4)

[tex]k(x)=x^2 +4x-1\\\\D=(4)^2-4\times 1\times (-1)\\\\D=20[/tex]

D>0  the roots are real and unequal

Function (5)

[tex]p(x)=5x^2 +5x+4\\\\D=(5)^2-4\times 5\times 4\\\\D=-55[/tex]

D<0  the roots are real and unequal

Function (6)

[tex]t(x)=x^2 -2x-15\\\\D=(-2)^2-4\times 1\times (-15)\\\\D=64[/tex]

D>0  the roots are real and unequal

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

Answer:

1,3,4,6

Step-by-step explanation:

EDGE

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