Without solving, determine the character of the solutions of the equation.
-$$f ( x ) = x ^ { 2 } + 3 x - 7$$
A) two complex solutions that are conjugates of each other
B) a repeated real solution
C) two unequal real solutions

Question

Quizplus · Accepted Answer

To determine the character of the solutions of the given quadratic equation $f(x) = x^2 + 3x - 7$, we look at the discriminant, $D = b^2 - 4ac$, where $a = 1$, $b = 3$, and $c = -7$. Calculating the discriminant, $D = 3^2 - 4(1)(-7) = 9 + 28 = 37$, which is positive. Therefore, the equation has two unequal real solutions.

Without Solving, Determine the Character of the Solutions of the Equation