Frame the equation whose root is -5+/-2root3

Answer 1

Lee, it’s easy to make such an equation. If you know two roots (let’s call them a and b), then the equation

(x-a)(x-b) = 0

is what you want.

We have two roots

( -5 + 2root3))

And

( -5 - 2root3))

So, plug the different roots in for a and b.

(x - ( -5 + 2root3)) (x - (-5 - 2root3)) = 0

Then simplify...

(x + 5 -2root3)) (x + 5 + 2root3)) = 0

And multiply it out

x² + 5x + x*2root3

+ 5x + 25 + 10root3

-2x*root3 -10root3 -4*root3*root3

simplify it

x² + 10x

+ 25

- 4*3

and simplify further

x² + 10x+ 13

To cross check this answer, use the quadratic formula

x = (-b +/- root(b²-4ac)) / 2a

x = (-10 +/- root(100 -4*13)) /2

x = (-10 +/- root(48)) /2

x = (-5 +/- 2root3)

That’s how to do it, Lee. If you have more questions please ask!