Find the value of c that makes each trinomial a perfect squa

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square. X^2 + 11x + c c = 121/4; (x - 11/2)^2 c = 121; (x + 11)^2 c = 121/4;(x + 11/2)^2 c = 121/2; (x + 11/4)^2

Solution

x² + 11x + c

We know that a perfect square is of the form:

(x + a)² = x² + a² + 2ax

Now comparing this result with the given equation:

2a = 11

a = 11 / 2

Hence, c = a² = (11/2)²

c = 121/4

The perfect square is:

(x + 11/2 )²

Hence, option (C). c = (121/4) , (x + 11/2)². is correct.