Question 758133: find the value of k in 2x^2 - 3(k^2)x = 8 - 6kx if one root is negative of the other.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! If the roots are negatives of each other, then the quadratic can be factored as
(x+r)(x-r) = 0 with roots r, -r
The quadratic is a difference of squares:
x^2 - r^2 = 0
The standard form for a quadratic is ax^2 + bx + c = 0
In this case the linear term, b = 0
Combining like terms in the equation gives
2x^2 - x(3k^2+6k) - 8 = 0
For the linear term to be zero, 3k^2 + 6k must equal zero:
3k^2 + 6k = 0
3k(k+2) = 0
This gives k=0, k=-2
Check:
k = 0,2 -> 2x^2 - 8 = 0 -> x = 2, -2
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