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

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.

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Shawn H. | Certified Teacher Specializing in MS, HS, and college mathCertified Teacher Specializing in MS, HS...
4.8 4.8 (46 lesson ratings) (46)

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.
So the last term of the trinomial must be 121/4 (choice B).

Good Luck,

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)

Completing the square,

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

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