Final answer:
The least possible value of n in the equation x^2-34x+c=0 can be found by setting the discriminant to be negative. Simplifying the inequality gives us c > 289.
Step-by-step explanation:
In the given equation, x^2-34x+c=0, if the equation has no real solutions when c is greater than n, we need to find the least possible value of n.
To determine the least possible value of n, we need to find the discriminant of the equation. The discriminant is given by the formula discriminant = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation. In this case, a=1, b=-34, and c=1.
Substituting the values in the discriminant formula, we get: discriminant = (-34)^2 - 4(1)(c). For the equation to have no real solutions, the discriminant must be negative. Therefore, we have (-34)^2 - 4(1)(c) < 0. To find the least possible value of n, we need to find the maximum value of c that satisfies this inequality.
Simplifying the inequality gives us: 1156 - 4c < 0. Solving this inequality, we get c > 289. Therefore, the least possible value of n is 289.