Find the value of k if x^2 + kx - 6 = (x - 2)(x + 3).

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equation.

x^2 + kx -6 = (x-2)(x+3)

We need to find the values of k.

First we will simplify the right side by opening the brackets.

==> x^2 + kx -6 = x^2 +3x -2x - 6

==> x^2 + kx -6 = x^2 + x - 6

Now we will add 6 to both sides.

==> x^2 + kx = x^2 + x

Now we will subtract x^2 from both sides.

==> kx = x

Now we will divide by x .

==> k = x/x = 1

==> Then the values of k = 1.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find k for x^2 + kx - 6 = (x-2)(x+3)

x^2 + kx - 6 = (x-2)(x+3)

=> x^2 + kx - 6 = x^2 - 2x + 3x - 6

=> x^2 + kx  - 6 = x^2 + x - 6

=> x^2 - x^2 - 6 + 6 + kx = x

=> kx = x

=> k = 1

The required value of k is k = 1

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