In the given expression x² - 7x - 18, what type of roots will the equation yield?

To determine the type of roots for the quadratic equation given by the expression ( x^2 - 7x - 18 ), we can apply the quadratic formula, which is:

[

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

]

In this case, the coefficients are ( a = 1 ), ( b = -7 ), and ( c = -18 ). The key part of the quadratic formula that tells us about the nature of the roots is the discriminant, given by ( b^2 - 4ac ).

Calculating the discriminant:

1. Compute ( b^2 ):

[

(-7)^2 = 49

]

2. Compute ( 4ac ):

[

4 \cdot 1 \cdot (-18) = -72

]

3. Combine these results to find the discriminant:

[

49 - (-72) = 49 + 72 = 121

]

The value of the discriminant is 121, which is greater than zero. A positive discriminant indicates that there are two distinct real