Question

How many real roots are there for the equation, x^2+4x-1=0 I think the answer is two real roots

Answer 1

2 real roots

Explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

Then the nature of the roots are found using 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 + 4x - 1 = 0 ← is in standard form

with a = 1, b = 4, c = - 1, then

b² - 4ac = 4² - (4 × 1 × - 1 ) = 16 + 4 = 20

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