You got negative values in the square root because this quadratic has two complex solutions. Continue on your way.
Checck the discriminat, . If it's negative, there are no real roots.
.........yep, negative discriminant, so only complex solutions.
Hello, Patrick_John!
There is a back-door approach to this problem
. . if you know some polynomial theory.
We want the value of: . .[A]Let be the two solutions of the quadratic equation: .
Find the value of: .
The equation is: .
Then: .
. . So we have: .
Substitute [2] and [3] into equation [A]: .
Hello, Patrick_John!
It's part of the theory . . .Why is the 2 in negative?
Instead of confusing you with symbols, I'll use specific examples
. . and hope you catch the pattern.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
For example: we are given a cubic equation: .
Divide by the leading coefficient and insert alternating signs.
. .
. .+ . . - . . .+ . . -
Suppose are the roots of the cubic.
Taking the roots one-at-a-time, their sum is: .
. . That is: .
Taking the roots two-at-a-time, their sum is: .
. . That is: .
Taking the roots three-at-a-time, their sum is: .
. . That is: .
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Suppose we are given a quartic equation: .
. . with roots .
Divide by the leading coefficient and insert alternating signs:
. .
. .+ . . - . . .+ . . .-. - .+
Take the roots . . .
Get it?