what is he value of c so that x^2 +7x + c is a perfect square trinomial?
a 14
b 7/2
c 7/4
d 49/4
To determine the value of c, we need to use a technique called "completing the square".
First, we write the trinomial in the form of (x + a)^2 for some value of a:
x^2 + 7x + c = (x + a)^2
Expanding the right-hand side gives:
x^2 + 2ax + a^2 = x^2 + 7x + c
We can see that the coefficient of x on both sides must be equal:
2a = 7
Solving for a gives:
a = 7/2
Substituting this value of a back into our equation:
x^2 + 7x + c = (x + 7/2)^2
Expanding the right-hand side gives:
x^2 + 2(7/2)x + (7/2)^2 = x^2 + 7x + c
Simplifying:
x^2 + 7x + 49/4 = (x + 7/2)^2
Therefore, the value of c that makes x^2 + 7x + c a perfect square trinomial is 49/4.
The answer is (d) 49/4.