Quadratic Equation

Question

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

Answer 1

If the roots are -3 and 4, we have x = -3 and x = 4. We can rewrite these as x + 3 = 0 and x - 4 = 0. Multiplying these equations gives us (x + 3)(x - 4) = 0(0) = 0, or x^2 -4x + 3x - 12 = x^2 -x -12 = 0. Since the leading coefficient is 1, we have our answer.