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.
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.
Hi Brittani,
We know that a perfect square trinomial must either look like a^{2 }+ 2ab + b^{2} or a^{2 }- 2ab + b^{2}. We can tell that your question uses the second form because the second term in x^{2}-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 b^{2}, so you will have to square both sides of the previous equation.
b^{2}=(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