Question

Write the quadratic equation whose roots are -6 and -4, and whose leading coefficient is 3.

Answer 1

Answer: 3x^2+30x+72

If you were to solve it:

3x^2+30x+72

1. Multiply 72 by leading coefficient (3) to get 216

2. 216 has factors of 12 and 18 which add up to thirty (the leading coefficient in the middle term)

3. Therefore it is factored to (x+12)(x+18)

4. Now divide each constant by three to get (x+4)(x+6)

5. Set each equal to zero to get roots
x= {-4,-6}