Help me please

Roots

1-In the equation x^{2}-5x+10=0, are the roots real or imaginary?

2-In the equation x^{2}-5x+10=0 are the roots equal or unequal?

3- In the equation x^{2}-5x+10=0 are the roots rational, irrational, or neither?

ManuelBautista2019
Mar 8, 2018

#1**-1 **

are any numbers ever truly real...ya know ya can't feel them, and sure they make up measurments but when you get down to it they are just an idea, not somethin you can hold like wood. heh funny right

ClownPrinceofChaos
Mar 8, 2018

#2

#3**-1 **

alrighty I happen to be in geometry at the moment so let me see what I can do

ClownPrinceofChaos
Mar 8, 2018

#4**0 **

Hi, ManuelBautista2019!

The discriminant of a quadratic equation is the expression of the radicand of the quadratic formula \(x ={-b \pm \sqrt{\textcolor{red}{b^2-4ac}} \over 2a}\). In the given quadratic equation x^2-5x+10, a=1, b=-5, and c=+10. The discriminant will allow you to answer every question here.

Let's see the value of the discriminant and interpret its meaning.

\(x^2-5x+10\\ a=1,b=-5,c=10\\ b^2-4ac\\ (-5)^2-4*1*10\\ 25-40\\ -15 \)

1) The discriminant of the original quadratic yields a negative value, as calculated above, so the roots are imaginary.

2) The roots of a quadratic can be equal if and only if the discriminant equals 0, so the roots are unequal.

3) We already determined that the roots are imaginary (look at #1), so the roots are neither of the options listed.

TheXSquaredFactor
Mar 8, 2018