To find the roots of the quadratic equation x² + 7x + 10 = 0, we can use the factoring method.
First, we need to factor the quadratic expression. We are looking for two numbers that multiply to 10 (the constant term) and add up to 7 (the coefficient of the x term).
The numbers that fit these criteria are 2 and 5, since 2 × 5 = 10 and 2 + 5 = 7.
This allows us to factor the equation as follows:
(x + 2)(x + 5) = 0
Next, we set each factor equal to zero to find the roots:
- x + 2 = 0 ⇒ x = -2
- x + 5 = 0 ⇒ x = -5
Therefore, the roots of the equation x² + 7x + 10 = 0 are x = -2 and x = -5.