Question 7 (2 points) Use discriminants to determine which of the following functions have at least one real root. Check all that apply. f(x)=-3x^2+x-2 b f(x)=-x^2+4 C f(x)=2x^2-12x+18 d f(x)=x^2-3x+25 e f(x)=10x^2-4x f f(x)=-x^2+10x-14

To determine which of the given functions have at least one real root, we need to calculate the discriminant for each function. The discriminant is given by the formula: where , , and are the coefficients of the quadratic equation .Let's calculate the discriminant for each function:a) \( f(x) = -3x^2 + x - 2 \) b) \( f(x) = -x^2 + 4 \) c) \( f(x) = 2x^2 - 12x + 18 \) d) \( f(x) = x^2 - 3x + 25 \) e) \( f(x) = 10x^2 - 4x \) f) \( f(x) = -x^2 + 10x - 14 \) Now, let's determine which functions have at least one real root based on the discriminant values:- If , the quadratic equation has two distinct real roots.- If , the quadratic equation has one real root (a repeated root).- If , the quadratic equation has no real roots.Based on the discriminant values, the functions that have at least one real root are:b) \( f(x) = -x^2 + 4 \)c) \( f(x) = 2x^2 - 12x + 18 \)e) \( f(x) = 10x^2 - 4x \)f) \( f(x) = -x^2 + 10x - 14 \)Therefore, the correct answers are:b) \( f(x) = -x^2 + 4 \)c) \( f(x) = 2x^2 - 12x + 18 \)e) \( f(x) = 10x^2 - 4x \)f) \( f(x) = -x^2 + 10x - 14 \)