What is the value of c so that x² – 11x + c is a perfect-square trinomial?

Question

The choices that i get are a) 121 b) 121/4 c) -11/2 d) 121/2

I've tried everyone of them and they don't make any sense.

Answer 1

Hi Brittani,

We know that a perfect square trinomial must either look like a² + 2ab + b² or a² - 2ab + b².  We can tell that your question uses the second form because the second term in x²-11x+c  is negative.

The key is to set -11x equal to -2ab since they are both the middle term of the  trinomial.
-11x = -2ab
In your example, a must equal x, since x is the square root of the first term.  Substitute into the equation.
-11x = -2(x)b
Next, divide both sides by -2x in order to isolate b.  Simplify by cancelling the negatives and the x's.
11/2 = b

The last term of the trinomial is equal to b², so you will have to square both sides of the previous equation.
b²=(11/2)²=121/4
So the last term of the trinomial must be 121/4 (choice B).

Good Luck,
Shawn

Answer 2

Completing the square,

x² – 11x + c = [x - (11/2)]^2 = x^2 - 11x + 121/4

Therefore, c = (11/2)^2 = 121/4