Question

write the quadratic equation whose roots are $-2$ and $-4$, and whose leading coefficient is 3. (use the letter $x$ to represent the variable.) $square=0$

Explanation:

Step1: Start from root form

If roots are $r_1=-2$ and $r_2=-4$, the basic quadratic is $(x - r_1)(x - r_2) = 0$, so:
$(x - (-2))(x - (-4)) = (x+2)(x+4)$

Step2: Expand the binomials

Multiply the two factors:
$(x+2)(x+4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8$

Step3: Apply leading coefficient

Multiply the entire polynomial by the leading coefficient 3:
$3(x^2 + 6x + 8) = 3x^2 + 18x + 24$

Answer:

$3x^2 + 18x + 24$