Question

write the quadratic equation whose roots are -1 and 6, and whose leading coefficient is 5. (use the letter x to represent the variable.)

Explanation:

Step1: Start with root factors

If roots are $r_1=-1$ and $r_2=6$, the factor form is $(x - r_1)(x - r_2) = (x+1)(x-6)$

Step2: Expand the factor form

$$(x+1)(x-6) = x^2 -6x +x -6 = x^2 -5x -6$$

Step3: Multiply by leading coefficient

Multiply the expanded polynomial by 5:
$$5(x^2 -5x -6) = 5x^2 -25x -30$$

Answer:

$5x^2 -25x -30 = 0$