Is 5x^2+2x+3=0 real or complex

the roots are complex

Step-by-step explanation:

Given a quadratic equation in standard form; ax² + bx + c = 0 : a ≠ 0

Then the discriminant Δ = b² - 4ac informs about the nature of the roots

• If b² - 4ac > 0 then roots are real and distinct

• If b² - 4ac = 0 then roots are real and equal

• If b² - 4ac < 0 then roots are complex

5x² + 2x + 3 = 0 ← is in standard form

with a = 5, b = 2, c = 3, thus

b² - 4ac = 2² - (4 * 5 * 3) = 4 - 60 = - 56

Since b² - 4ac < 0 then roots are complex