The quadratic equation equivalent to the expression x² + 5x + 6 = 0 can be determined by examining its components.
To start, let’s rewrite the equation in standard form:
x² + 5x + 6 = 0
This equation is already in the standard quadratic format of ax² + bx + c = 0, where:
- a = 1
- b = 5
- c = 6
Next, we can factor the quadratic equation to see if it simplifies further. We are looking for two numbers that multiply to give c (6) and add up to b (5). The numbers 2 and 3 meet this criteria:
(x + 2)(x + 3) = 0
Thus, the quadratic equation can also be expressed as:
(x + 2)(x + 3) = 0
To summarize, the equivalent quadratic equation to x² + 5x + 6 = 0 is:
(x + 2)(x + 3) = 0
This means that the roots of the equation are x = -2 and x = -3.