Question

X2+ 8x + 13=0
discriminat
Number of roots
Types of roots

Answer 1

2 real and distinct roots

Explanation:

Given a quadratic equation in standard form

ax² + bx + c ( a ≠ 0 )

Then the nature of the roots are given by the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real and distinct roots

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then 2 complex roots

x² + 8x + 13 = 0 ← is in standard form

with a = 1, b = 8, c = 13 , then

b² - 4ac = 8² - (4 × 1 × 13) = 64 - 52 = 12

Since b² - 4ac > 0 then the equation has 2 real and distinct roots