Question

-5x^2+4x-9 меньше или равно 0

Answer 1

-5х²+4х-9 ≤ 0
1. у = -5х²+4х-9
график является параболой, ветви которой направлены вниз, так как старший коэффициент а < 0.
2. -5х²+4х-9 = 0
D = 16-4×(-5)×(-9) = -164
корней нет, так как D < 0
3. Х принадлежит (-∞, +∞)

Answer 2

To solve the inequality, you need to find the values of x for which the expression -5x^2 + 4x - 9 is less than or equal to zero.

The inequality is: -5x^2 + 4x - 9 ≤ 0

Step 1: Set the expression equal to zero to find the critical points (where the expression changes sign): -5x^2 + 4x - 9 = 0

Step 2: Solve the quadratic equation. However, it seems this quadratic equation cannot be factored easily, so let's use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

For our equation -5x^2 + 4x - 9 = 0, a = -5, b = 4, and c = -9: x = (-(4) ± √((4)^2 - 4(-5)(-9))) / 2(-5) x = (-4 ± √(16 - 180)) / (-10) x = (-4 ± √(-164)) / (-10)

Step 3: Since the discriminant (the value inside the square root) is negative, there are no real solutions for x in the equation -5x^2 + 4x - 9 = 0. Therefore, the expression -5x^2 + 4x - 9 does not intersect the x-axis, and the sign of the expression remains the same on both sides of the critical points.

Step 4: To determine the sign of the expression in different intervals, you can either use test points or analyze the behavior of the quadratic function. Since we know the coefficient of x^2 is negative (-5), the parabola opens downwards, indicating that the expression will be positive in the regions outside of the roots and negative in the region in between.

In summary, the solution to the inequality -5x^2 + 4x - 9 ≤ 0 is that there are no real solutions for x to satisfy the inequality. The expression is never less than or equal to zero, so there are no x values that fulfill this condition. Visually, the parabola representing the expression does not intersect or touch the x-axis, remaining above the x-axis for all x values.