help with a quadratic equation question

One of the roots of the equation x^{2} + kx -6 = 0 is 3, and k is constant. Which is greater: k or -1

Now if you plug in 3 for x you get -1 which makes sense, but when I first did the problem I tried to solve it by factoring the equation and I came up with k= -1 or 1 as shown below.

(x + 3)(x - 2) = x^{2} + x - 6 here k = 1

(x - 3)(x + 2) = x^{2} - x - 6 here k = -1

where am I going wrong? thank you for the help

Re: help with a quadratic equation question

Hello, buckethdd!

Quote:

One of the roots of the equation x^{2} + kx -6 = 0 is 3, and k is constant.

Which is greater: k or -1 ?

Now if you plug in 3 for x, you get -1, which makes sense,

but when I first did the problem I tried to solve it by factoring the equation

and I came up with k= -1 or 1 as shown below.

(x + 3)(x - 2) = x^{2} + x - 6 here k = 1 . The roots are -3 and 2.

(x - 3)(x + 2) = x^{2} - x - 6 here k = -1

Where am I going wrong? thank you for the help.