Question

write the quadratic equation whose roots are -3 and 6, and whose leading coefficient is 3. (use the letter x to represent the variable.) \\(\square = 0\\)

Explanation:

Step1: Start with root form

If roots are $r_1=-3$ and $r_2=6$, the basic quadratic is $(x - r_1)(x - r_2)=0$, so:
$(x - (-3))(x - 6)=0$
$(x+3)(x-6)=0$

Step2: Expand the binomials

Multiply the two factors:
$x^2 -6x +3x -18=0$
$x^2 -3x -18=0$

Step3: Apply leading coefficient 3

Multiply the entire equation by 3:
$3(x^2 -3x -18)=0$
$3x^2 -9x -54=0$

Answer:

$3x^2 -9x -54$