find the value of c that makes each trinomial a perfect square. then write the trinomial as a prefect square.
x^2-10x+c
x^2+60x+c
x^2-10x+c
-10/2=-5
-5*-5=25
so x^2-10x+25
is that corrrect??
and the other would be x^2+60x+900
both correct
To find the value of c that makes each trinomial a perfect square, we can use the completion of square method.
For the trinomial x^2 - 10x + c to be a perfect square, we need to find the value of c that completes the square.
Step 1: Take half of the coefficient of x (-10) and square it: (-10/2)^2 = 25.
Step 2: The value of c that completes the square is 25, since (x - 5)^2 = x^2 - 10x + 25.
Therefore, c = 25, and the trinomial x^2 - 10x + 25 is a perfect square.
Similarly, for the trinomial x^2 + 60x + c to be a perfect square, we follow the same steps.
Step 1: Take half of the coefficient of x (60) and square it: (60/2)^2 = 900.
Step 2: The value of c that completes the square is 900, since (x + 30)^2 = x^2 + 60x + 900.
Therefore, c = 900, and the trinomial x^2 + 60x + 900 is a perfect square.