Question

Find the value of c such that the expression is a​ perfect-square trinomial.

k^2 -3k+c
k^2 -3k+c=k^2 -3k+__ ​(Type an integer or a simplified​ fraction.)

Answer 1

To make the expression a perfect square trinomial, we need to add and subtract the square of half of the coefficient of k. In this case, the coefficient of k is -3. Half of -3 is -3/2. The square of -3/2 is 9/4. Therefore, we can add and subtract 9/4 to the expression as follows:

• k^2 -3k+c = k^2 -3k+9/4-9/4+c

Now we can write this as a perfect square trinomial:

• (k-3/2)^2 + (c-9/4)
• Therefore, c-9/4 must be equal to 0 for the expression to be a perfect square trinomial. This means that c=9/4.

So, the value of c such that the expression is a perfect-square trinomial is 9/4.