Final answer:
The quadratic equation with roots -1 and 3 and a leading coefficient of 4 is 4x² - 8x - 12 = 0.
Step-by-step explanation:
The student is asking for the equation of a quadratic equation whose roots are -1 and 3, and whose leading coefficient is 4.
To find this equation, we can use the fact that if p and q are the roots of the quadratic equation ax² + bx + c = 0, then the equation can be written as a(x - p)(x - q) = 0.
In this case, our p and q values are -1 and 3, so the equation is 4(x + 1)(x - 3) = 0.
Expanding this out, we get 4x² - 8x - 12 = 0, which is the standard form of the quadratic equation we are looking for.