what is the value of c so that x^2+13x+c is a perfect square trinomial
I need HELP ASAP!!!
take 1/2 of the coefficient of the middle term, then square it, so
c = 169/4
To determine the value of c so that the quadratic expression x^2 + 13x + c is a perfect square trinomial, we need to follow these steps:
Step 1: Divide the coefficient of x by 2 and square the result.
(13 / 2)^2 = 169 / 4 = 42.25
Step 2: The value of c should be the squared result from Step 1 to make the expression a perfect square trinomial.
Therefore, c = 42.25.
So, the value of c that makes the quadratic expression x^2 + 13x + c a perfect square trinomial is 42.25.
To find the value of c such that x^2 + 13x + c is a perfect square trinomial, we need to manipulate the expression and use a specific property.
Step 1: Recall that for a perfect square trinomial in the form a^2 + 2ab + b^2, both a and b must be equal.
In our case, we have x^2 + 13x + c (where a = x and b = √c).
Step 2: We will compare the given expression, x^2 + 13x + c, with the perfect square trinomial, a^2 + 2ab + b^2, by looking at the coefficients of x and the constant term.
- The coefficient of x^2 is 1, which should be equal to a^2.
- The coefficient of x is 13, which should be equal to 2ab.
- The constant term is c, which should be equal to b^2.
Step 3: Set up the equations using the observations from Step 2:
Equation 1: 1 = a^2
Equation 2: 13 = 2ab
Equation 3: c = b^2
Step 4: Solve for a and b from Equation 1 and Equation 2:
Equation 1: 1 = a^2 => a = ±√1 => a = ±1
Equation 2: 13 = 2ab => b = 13/(2a) => b = 13/(2 * ±1) => b = 13/±2
Step 5: Plug the values of a and b into Equation 3 to solve for c:
c = b^2 => c = (13/±2)^2 => c = 169/4
Therefore, the value of c that makes the expression x^2 + 13x + c a perfect square trinomial is c = 169/4.