SOLUTION: For what values of k will the equation {{{ x^2 -(k-2)x-12=0}}} have roots that are equal but opposite in sign

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Question 1013006: For what values of k will the equation have roots that are equal but opposite in sign
Found 3 solutions by ikleyn, Theo, MathLover1:
Answer by ikleyn(52798)   (Show Source):
You can put this solution on YOUR website!
.
For k = 2.

In this case the line x = 0 is the symmetry line for the parabola.

You can deduce it from the quadratic formula too.

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
when k = 2, the equation of x^2 - (k-2)x - 12 = 0 becomes x^2 - -0x - 12 = 0 which becomes x^2 - 12 = 0.
add 12 to both sides of this equation to get x^2 = 12.
take the square root of this equation to get x = plus or minus sqrt(12).

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

to have roots that are equal but opposite in sign, we can write our equation like this:

And since we started with
we can set the left sides equal:
....solve for

check:

solutions: and