Question

Using the discriminant, how many real number solutions does this equation have?

3x^2 – 2 = 5x

Answer 1

3 x² – 2 = 5 x

3 x² – 2 - 5 x = 0

3 x² - 5 x - 2 = 0

a x² + b x + c = 0

in this case:

a = 3 , b = - 5 , c = - 2

D = b² - 4 ∙ a ∙ c

D = ( - 5 )² - 4 ∙ 3 ∙ ( - 2 )

D = 25 + 4 ∙ 3 ∙ 2

D = 25 + 24

D = 49


If D > 0, the equation has 2 real solutions.

If D = 0, the equation has 1 real solution.

If D < 0, the equation has 2 conjugate imaginary solutions.

In this case D > 0 , so the equation has 2 real solutions.