The quadratic 2x^2-3x+27 has two imaginary roots. What is the sum of the squares of these roots? Express your answer as a decimal rounded to the nearest hundredth.

Please Help Quick!

Guest Dec 16, 2020

#1**0 **

**Why do you need help so quickly?**

Are you doing a test?

Have you left your homework till the last minute and need someone else to do it for you?

Melody Dec 16, 2020

#2**-1 **

No, I'm doing an AoPs question, and I have tried to do it myself but I just don't know how to find the roots. Also, this work is due in January, and I am just bored and wondering if I can learn new things by doing a bit of work ahead of time. If you could help me with that it would be much appreciated. Thank you!

Guest Dec 16, 2020

#3**0 **

Use the Quadratic formula to find the roots

a=2 b =-3 c = 27

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) then x = 3/4 +- 3/4 * i sqrt23

squaring them results in 9/16 +~~18/16 sqrt23 i ~~- 9/ 16 * 23 and 9/16 -~~ 18/16 sqrt23 i~~ - 9/16*23

then adding them = - 198/8 = -99/4

Guest Dec 17, 2020

#4**+1 **

Call the roots m and n

By Vieta's Theorem......

ax^2 + bc + c

Sum of roots = m + n = -b/a = 3/2 square both sides m^2 + 2mn + n^2 = 9/4 (1)

Product of roots = mn = c/a = 27/2 and 2mn = 27 (2)

So......subbing (2) into ( 1) we have

m^2 + 27 + n^2 = 9/4

m^2 + n^2 = 9/4 - 27

m^2 + n^2 = [9 - 108 ] / 4 = - 99 / 4

CPhill Dec 17, 2020