Question
Use the discriminant to determine the number of real solutions of 5=2x−x2
.(1 point)
real solution(s)
To find the discriminant in this case, we need to rewrite the equation in the form ax^2 + bx + c = 0.
Rearranging the equation, we have -x^2 + 2x - 5 = 0.
Now we can compare this equation to the standard form ax^2 + bx + c, where a = -1, b = 2, and c = -5.
The discriminant (D) of a quadratic equation is given by the formula D = b^2 - 4ac.
Plugging in the values, we have D = (2)^2 - 4(-1)(-5).
Simplifying, D = 4 - 20 = -16.
Since the discriminant is negative (D < 0), there are no real solutions to the equation -x^2 + 2x - 5 = 0.
Therefore, the number of real solutions is 0.