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

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2 Answers

Hi Brittani,

We know that a perfect square trinomial must either look like a+ 2ab + b2 or a- 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

Completing the square,

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

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