What is the value of c that makes this trinomial a perfect square?
x^2 + 15x + c
To determine the value of c that makes the trinomial a perfect square, we can use the formula for the perfect square trinomial.
The formula for a perfect square trinomial of the form x^2 + bx + c is (x + (b/2))^2.
In this case, we have x^2 + 15x + c. To match the formula, we want the coefficient of x to be (b/2), which means (b/2)^2 should be equal to c.
Given that b = 15, we can calculate (b/2)^2 as follows:
(15/2)^2 = 7.5^2 = 56.25.
Therefore, c should be equal to 56.25.
To determine the value of c that makes the trinomial a perfect square, we need to follow these steps:
Step 1: Start with the given trinomial: x^2 + 15x + c.
Step 2: To create a perfect square trinomial, we want the first term (x^2) to remain unchanged. So, we need to focus on the second term (15x).
Step 3: Take half of the coefficient of the second term (15x) and square it. Half of 15x is (15/2)x, and (15/2)^2 is (225/4)x^2.
Step 4: The value of c that makes the trinomial a perfect square is equal to the result obtained in step 3, which is (225/4).
Therefore, the value of c that makes the trinomial x^2 + 15x + c a perfect square is (225/4).