Hello
Let be the two solutions of the quadratic equation
Then the value of is ?
How can I get the values for and ? After trying with the quadratic ecuation, I was always getting a negative value on the section.
Thanks.
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: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Suppose we are given a quartic equation: .
. . with roots .
Divide by the leading coefficient and insert alternating signs:
. .
. .+ . . - . . .+ . . .-. - .+
Take the roots . . .
Get it?