Question

Пж решите X^2-5x-50<0

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the quadratic inequality $x^2 - 5x - 50 < 0$, we can use the method of factoring.

First, let's rewrite the inequality as an equation:

$x^2 - 5x - 50 = 0$

Next, we need to find the roots of this equation by factoring or using the quadratic formula. The roots are the points where the quadratic function equals zero.

The quadratic equation can be factored as:

$(x - 10)(x + 5) = 0$

Setting each factor equal to zero, we have:

$x - 10 = 0$ or $x + 5 = 0$

Solving for $x$ in each equation, we find:

$x = 10$ or $x = -5$

These are the x-intercepts of the quadratic function.

Now, let's analyze the sign of the quadratic expression $x^2 - 5x - 50$ in different intervals:

Interval 1: $(-\infty, -5)$ Choose a test point, for example, $x = -6$: $(-6)^2 - 5(-6) - 50 = 36 + 30 - 50 = 16$ Since 16 is positive, the quadratic expression is positive in this interval.

Interval 2: $(-5, 10)$ Choose a test point, for example, $x = 0$: $0^2 - 5(0) - 50 = -50$ Since -50 is negative, the quadratic expression is negative in this interval.

Interval 3: $(10, +\infty)$ Choose a test point, for example, $x = 11$: $11^2 - 5(11) - 50 = 121 - 55 - 50 = 16$ Since 16 is positive, the quadratic expression is positive in this interval.

Finally, we can conclude that the inequality $x^2 - 5x - 50 < 0$ is true when $x$ belongs to the interval $(-5, 10)$.

In interval notation, the solution is $(-5, 10)$.