Question

Determine whether the rational root theorem provides a complete list of all roots for the following polynomial functions. f(x) = 4x2 − 25 g(x) = 4x2 + 25 h(x) = 3x2 − 25

Answer 1

Answer:

on Quizlet:  1) yes   2) no, complex roots  3) no, irrational roots

Step-by-step explanation:

Answer 2

Answer:

f(x)=x=±$\frac{\sqrt{25} }{2}$ represents all its roots.

g(x)=x=±$\frac{\sqrt{-25} }{2}$ does not represent roots

because negative number cannot exist in under root

h(x)=±$\sqrt{\frac{25}{3} }$ represents all its roots

Step-by-step explanation:

#1

f(x)=$4x^{2}$-25

to find rational root we will put  $4x^{2}$-25=0

$4x^{2}$=25

$x^{2}$=$\frac{25}{4}$

f(x=)x=±$\sqrt{\frac{25}{4} }$

f(x)=x=±$\frac{\sqrt{25} }{2}$

#2

g(x)=$4x^{2}$+25

to find rational root we will put  $4x^{2}$+25=0

$4x^{2}$=-25

$x^{2}$=$\frac{-25}{4}$

g(x=)x=±$\sqrt{\frac{-25}{4} }$/

#3

h(x)=$3x^{2}$-25

to find rational root we will put  $3x^{2}$-25=0

$3x^{2}$=25

$x^{2}$=$\frac{25}{3}$

h(x=)x=±$\sqrt{\frac{25}{4} }$

h(x)=±$\sqrt{\frac{25}{3} }$