What are the Roots of the Original Quadratic Equation

The correct quadratic equation is ax² + bx - 6 = 0
The erroneous quadratic equation is ax² + bx + 6 = 0
 

From ax² + bx + 6 = 0, x₁ = -2 and x₂ = -3
Product of roots:   $x_1 \, x_2 = \dfrac{c}{a}$

$-2(-3) = \dfrac{6}{a}$

$a = 1$
 

Sum of roots:   $x_1 + x_2 = -\dfrac{b}{a}$

$-2 - 3 = -\dfrac{b}{1}$

$b = 5$
 

Thus, the correct equation is x² + 5x - 6 = 0
$(x - 1)(x + 6) = 0$
$x = 1 ~ \text{and} ~ 6$