What is the value of c such that x^2-11x+c is a perfect-square trinomial?
A perfect-square trinomial is a trinomial that can be factored into a binomial squared form.
For a quadratic trinomial ax^2 + bx + c to be a perfect-square trinomial, the coefficient of x should be equal to twice the square root of c.
In this case, we have the trinomial x^2 - 11x + c.
The coefficient of x is -11, so it must be equal to 2 times the square root of c: -11 = 2√c.
To solve for c, we can isolate the square root term:
√c = -11/2
Squaring both sides to eliminate the square root, we have:
c = (-11/2)^2
c = 121/4
Therefore, the value of c such that x^2 - 11x + c is a perfect-square trinomial is 121/4.