Using the quadratic formula, find the exact value of x for the following.
-2kx^2 + 4x + 6k = 0
- a is whatever is in front of x^2 = -2k
- b is whatever is in front of x = 4
- c is whatever does not have an x with it = 6k
Simplify to give
There is no way to solve x for a number without knowing the value of k
Collecting and multiplying out the terms in the square root gives
As the HCF of 48 and 16 is 16 we can remove this as a factor: note, I made a mistake here in my other working - that +3 should have been a +1
Reintroducing this to the full equation:
Reintroducing the simplified discriminant:
4 will cancel to give
You can leave it like that but it's more usual to not have a negative denominator so we multiply by
Since there is a kČ term under the square root sign then x will be real for all real k
is quadratic in x (you just have to see it). To isolate x, use .