Question

Find the number of real solutions using the discriminant.
x² + 9x + 4 = 0

Answer 1

Calculate b^2-4ac

Answer 2

2

Answer 3

this is an interesting question as all quadratics will have 2 solutions.

b^2 - 4ac > 0 then the quadratic has 2 real unequal solutions if the value of b^2 - 4ac is a square number then the solutions are real and rational.

if b^2 - 4ac is not a square number the solution is irrational.

if b^2 - 4ac = 0 then the quadratic has a repeated or 2 equal solution. This is the case of the perfect square y = (x -a)^2

in your question you have

9^2 - 4 x 1 x 4 = 81 - 16

the discriminant = 65 there are 2 real irrational solutions