Final answer:
The standard form of the quadratic equation with roots of -6 and 4 is x² - 2x - 24 = 0.
Step-by-step explanation:
The standard form of a quadratic equation is ax² + bx + c = 0. Given the roots of -6 and 4, we can find the equation by using the fact that the roots are solutions to this equation. Since the roots are -6 and 4, the factors of the quadratic equation would be (x + 6) and (x - 4). Multiplying these two factors together gives us x² + 2x - 24, which matches option B.
The standard form of a quadratic equation with roots of -6 and 4 is option C) x^2 + 2x + 24 = 0.
To find the standard form, we use the fact that if a quadratic equation has roots r1 and r2, then it can be written as (x - r1)(x - r2) = 0. In this case, substituting -6 and 4 for r1 and r2, we get (x + 6)(x - 4) = 0.
Expanding the equation, we get x^2 + 2x - 24 = 0, which matches option C.
Therefore, the standard form of the quadratic equation with roots of -6 and 4 is x² - 2x - 24 = 0.