Question

write the quadratic equation whose roots are 4 and -3, and whose leading coefficient is 4. (use the letter x to represent the variable.) \\(\square = 0\\)

Explanation:

Step1: Start with root form

If roots are $r_1$ and $r_2$, the basic quadratic is $(x-r_1)(x-r_2)=0$. Substitute $r_1=4$, $r_2=-3$:
$(x-4)(x-(-3)) = (x-4)(x+3)$

Step2: Expand the binomials

Multiply the two factors:
$(x-4)(x+3) = x^2 + 3x - 4x - 12 = x^2 - x - 12$

Step3: Apply leading coefficient

Multiply the entire polynomial by the leading coefficient 4:
$4(x^2 - x - 12) = 4x^2 - 4x - 48$

Answer:

$4x^2 - 4x - 48 = 0$