How many real roots does the function f (x) = x^2+8x-2

First find the determinant, Δ = b^2 - 4ac

a = 1, b = 8, c = - 2

Δ = 8^2 - 4*1*-2

Δ = 64 + 8

Δ = 72 > 0

therefore there are two real roots!

Using the discriminant

for

f (x) = ax²+bx+c

the discriminant is b²-4ac

when it is

1. less than 0, there are no real roots

2. equal to 0, then there is 1 real root

3. more than 0, 2 real roots

given

f (x) = 1x²+8x-2

a=1

b=8

c=-2

discriminat

8²-4 (1) (-2)

64+8

this is greater than 0

2 real roots