Question

Помогите пж. при каких значениях х выражений -х²+6х принемает отрицательное значения

Answer 1

X²+6x<0
-x(x-6)<0
x(x-6)>0
метод интервалов
========0=========6========
++++++++  -----------------     +++++++++
x=(-oo 0)U(6 +oo)

Answer 2

Finding the Values of x for which the Expression -x² + 6x is Negative

To determine the values of x for which the expression -x² + 6x takes on negative values, we need to find the range of x that satisfies this condition.

The expression -x² + 6x represents a quadratic function. Quadratic functions can be graphed as a parabola, which opens downwards if the coefficient of the x² term is negative.

In this case, the coefficient of the x² term is -1, which means the parabola opens downwards. Therefore, the expression -x² + 6x will be negative in the range of x values where the parabola is below the x-axis.

To find the x-values where the expression is negative, we can set the expression equal to zero and solve for x. This will give us the x-values where the parabola intersects the x-axis. The values of x outside of these intersections will make the expression negative.

Let's solve for x:

-x² + 6x = 0

Factoring out an x:

x(-x + 6) = 0

Setting each factor equal to zero:

x = 0 or -x + 6 = 0

Solving for x in the second equation:

-x + 6 = 0 x = 6

So, we have two x-values: x = 0 and x = 6. These are the x-values where the expression -x² + 6x equals zero.

To determine the range of x-values where the expression is negative, we can test a value from each interval created by the x-intercepts.

Let's test a value less than 0, a value between 0 and 6, and a value greater than 6.

Testing x = -1: -x² + 6x = -(-1)² + 6(-1) = -1 - 6 = -7 Since -7 is negative, the expression is negative for x < 0.

Testing x = 1: -x² + 6x = -(1)² + 6(1) = -1 + 6 = 5 Since 5 is positive, the expression is positive for 0 < x < 6.

Testing x = 7: -x² + 6x = -(7)² + 6(7) = -49 + 42 = -7 Since -7 is negative, the expression is negative for x > 6.

Therefore, the expression -x² + 6x is negative for x < 0 and x > 6.

In summary: The expression -x² + 6x takes on negative values when x is less than 0 or greater than 6.

Please let me know if there's anything else I can help you with!