Question

Explain whether or not the plant labeled p(x)=x2+x+3 has any rational or irrational roots.

Answer 1

frational roots are those numbers that can be written in form $\frac{a}{b}$ where a and b are integers (integers are like -5,-4,-3,-2,-1,0,1,2,3,4, etc)

some examples are 1=1/1, 2=2/2, -4=-4/1, 4/3, 0.111111111111=1/9, etc

irrational numbers are numbers that can't be written that way like pi

numbers that involve √-1 or a square root of any negative number are called complex numbers and are neither rational nor irrational.

roots are the values of x that makes the function equal to 0

$p(x)=x^2+x+3$

set equal to 0

$0=x^2+x+3$

I can't factor so use quadratic formula

for $0=ax^2+bx+c$

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

so

$x=\frac{-1 \pm \sqrt{1^2-4(1)(3)}}{2(1)}$

$x=\frac{-1 \pm \sqrt{-11}}{2}$

√-11 is a square root of a negative number so it is a complex number. therefore, the function does not have rational or irrational roots

p(x) has no rational or irrational roots