In copying a second degree equation, a student mistakenly wrote the constant term as 6 instead of -6. His answers were -2 and -3. What are the answers to the original equation?

The correct quadratic equation is ax^{2 }+ bx - 6 = 0 The erroneous quadratic equation is ax^{2 }+ bx + 6 = 0

From ax^{2 }+ bx + 6 = 0, x_{1} = -2 and x_{2} = -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 x^{2} + 5x - 6 = 0 $(x - 1)(x + 6) = 0$ $x = 1 ~ \text{and} ~ 6$

Thank you

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The correct quadratic equation is ax

^{2 }+ bx - 6 = 0The erroneous quadratic equation is ax

^{2 }+ bx + 6 = 0From ax

^{2 }+ bx + 6 = 0, x_{1}= -2 and x_{2}= -3Product 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 x

^{2}+ 5x - 6 = 0$(x - 1)(x + 6) = 0$

$x = 1 ~ \text{and} ~ 6$

Thank you

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