Final answer:
To create a quadratic equation with roots of -12 and 2, one should start with the factored form (x + 12)(x - 2) = 0 and expand to achieve the standard form: x^2 + 10x - 24 = 0.
Step-by-step explanation:
To write a quadratic equation in standard form with roots of -12 and 2, we can use the fact that if p and q are roots of a quadratic equation, the equation can be expressed as ax^2 + bx + c = 0, where (x - p)(x - q) = 0.
Thus, for roots -12 and 2, the quadratic equation is:
(x + 12)(x - 2) = 0
Expanding this, we get:
x^2 - 2x + 12x - 24 = 0
Simplifying, we find the standard form:
x^2 + 10x - 24 = 0