To find a quadratic equation equivalent to the expression x² + 5x + 6, we can utilize factorization. A quadratic equation is typically in the form of ax² + bx + c = 0, and in this case, we have:
a = 1, b = 5, c = 6
We begin by looking for two numbers that multiply to c (6) and add up to b (5). The numbers 2 and 3 satisfy this condition because:
- 2 × 3 = 6
- 2 + 3 = 5
Using these factors, we can rewrite the quadratic equation as:
(x + 2)(x + 3) = 0
Thus, the equivalent quadratic equation in factored form is (x + 2)(x + 3) = 0. Expanding this gives back the original equation:
x² + 5x + 6 = 0
In conclusion, any quadratic equation equivalent to x² + 5x + 6 = 0 can be written as (x + 2)(x + 3) = 0.