For what values of k will the equation x(14^1/2) + 7 = kx^2 have exactly 2 real solutions? I am stuck so any help would be greatly appreciated!! Also, the 14^1/2 is just supposed to be the sqaure root of fourteen.
1 Answer
Explanation:
Arrange to get:
This is just a quadratic equation of the form
With
The discriminant of a quadratic is;
We know that for:
We need two real solutions, so we use:
Plugging in our known values:
Squaring:
We can check this. To make our life easier lets say
By quadratic formula:
These are both real and different, as expected.
Hope it helps.