SOLUTION: determine the value(s) of "k" for which there is one and only one real solution to the following quadratic: 10kx = -16x^2 - 25
Thank you
Algebra.Com
Question 707046: determine the value(s) of "k" for which there is one and only one real solution to the following quadratic: 10kx = -16x^2 - 25
Thank you
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
There will be one and only one real solution to a quadratic equation when the discriminant is zero. So let's start by putting the equation into standard form. Adding and 25 to each side:
The discriminant, in general, is . Our "a" is 16, "b" is 10k and "c" is 25. So our discriminant is:
which simplifies to:
We want this to be zero so:
Now we solve for k. Dividing both sides by 100:
Adding 12:
So or . These square roots simplify:
or
or
or
These are the only possible values for k which will lead to one and only one real solution for x.
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