Quadratic Equation

Question

Write the quadratic equation whose roots are
−1
and
−4
, and whose leading coefficient is
3
.
(Use the letter
x
to represent the variable.)

Answer 1

x=-1 implies x+1=0

x=-4 implies x+4=0

(x+1)(x+4)=0

x²+5x+4=0

3(x²+5x+4)=0

3x²+15x+12=0

Answer 2

If you want roots of:

x = -1

and

x = -4

move everything to the left side so they equal zero

x+1 = 0

x+4 = 0

For an equation to have both roots, multiply these together

(x+1)(x+4) = 0*0

When you multiply these together, the leading (x²) coefficient is 1, so you need to multiply everything by 3.