Question

Find the number of solutions of this equation using the discriminant.
x² - 9x + 4 = 0

Answer 1

If the discriminant (b^2 - 4ac) is positive = 2 solutions
If the discriminant is 0 = 1 solution
If negative = No REAL solution (only imaginary)

Answer 2

Our discriminant is:\[(-9)^{2}-4(1)(4)\]

Answer 3

or in other words:
(-9)(-9) - 4(1)(4)

This simplifies to:

81 - 16 = ??

So again, if the answer is positive, you will have: 2 Solutions.
If the answer is zero, you will have: 1 Solution.
If the answer is negative, you will have No Real Solutions (only imaginary solutions).

Hope that helped. Take care.