i)find one solution
ii) two
iii)none
Compare your equation to the standard form of a quadratic equation.
Quadratic:
Yours:
Assuming k is a constant we can match the coefficients:
The discriminant is given by:
If:
- then there are two, different, real solutions
- then there are two, equal, real solutions
- then there are no real solutions
I will let you figure out the rest of the question
For all of the above, you need to evaluate the discriminant.
.
For one solution, .
So
.
So or
or , for one solution.
No solutions: .
So .
To evaluate this, you will need to complete the square.
.
2 solutions: .
So .
To evaluate this, again you will need to complete the square.
or
or .