Find the value of "K" which will make the quadratic expression 9x^2 - 12x + k a perfect square

Answer 1

To determine the value of "k" which will make the quadratic expression a perfect square, we need to find the square of the binomial that will result in the quadratic expression.

Given expression: 9x^2 - 12x + k

The square of the binomial (ax + b)^2 is given by:

(ax + b)^2 = a^2x^2 + 2abx + b^2

Comparing the given expression with the square of the binomial:

a^2 = 9, 2ab = -12, b^2 = k

Since a^2 = 9, a = 3

Substitute the values of a and 2ab into the second equation:

2ab = -12
2(3)b = -12
6b = -12
b = -2

Now, find the value of "k" by squaring b:

b^2 = (-2)^2
b^2 = 4

Therefore, the value of "k" that will make the quadratic expression a perfect square is 4.