Find the value of K in 36x^2+18x+K.
To find the value of K in the quadratic equation 36x^2 + 18x + K, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Comparing the given equation to the general form of a quadratic equation, ax^2 + bx + c, we have a = 36, b = 18, and c = K.
Since we are trying to find the value of K, we can set x = 0 and solve for K. Plugging in the values into the quadratic formula, we have:
0 = (-18 ± √(18^2 - 4(36)(K))) / 2(36)
Simplifying further:
0 = (-18 ± √(324 - 144K)) / 72
To simplify the equation, let's focus on the discriminant, which is the term under the square root: 324 - 144K. For the quadratic equation to have real solutions, the discriminant must be greater than or equal to zero.
So,
324 - 144K ≥ 0
Rearranging the inequality:
144K ≤ 324
Solving for K:
K ≤ 324/144
Simplifying:
K ≤ 9/4
Therefore, the value of K in 36x^2 + 18x + K is less than or equal to 9/4.