Question

X^2-5x-6<0 решите пж

Answer 1

Сначала решаем как квадратное уравнение. x²-5x-6=0,  D=b²-4ac=25+24=49, √D=7, x1=(-b+√D)/2a=(5+7)/2=6, x2=(-b-√D)/2a=(5-7)/2=-2/2=-1. Точки -1 и 6 нарисуйте на координатной оси. Через эти точки проведи параболу рогами вверх. Та область, что ниже координатной оси и будет твоя область. В виде записи это выглядит так: -1∠x∠6. Удачи!

Answer 2

To solve the inequality $x^2 - 5x - 6 < 0$, we can use a method called "interval testing" or "sign chart."

Step 1: Find the critical points by setting the expression inside the inequality to zero and solving for $x$: $x^2 - 5x - 6 = 0$

Factorizing the quadratic equation: $(x - 6)(x + 1) = 0$

Setting each factor to zero and solving for $x$: $x - 6 = 0 \implies x = 6$ $x + 1 = 0 \implies x = -1$

Step 2: Create a sign chart to test the intervals between the critical points and beyond.

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     \(-\infty \quad -1 \quad 6 \quad +\infty\)
     \(+ \quad ? \quad ? \quad +\)

Step 3: Pick a test point from each interval and plug it into the inequality to determine the sign of the expression:

Let's pick $x = -2$ (a value less than -1): $x^2 - 5x - 6 = (-2)^2 - 5(-2) - 6 = 4 + 10 - 6 = 8 > 0$

The expression is positive (+) for $x < -1$.

Now, let's pick $x = 0$ (a value between -1 and 6): $x^2 - 5x - 6 = 0^2 - 5(0) - 6 = -6 < 0$

The expression is negative (-) for $-1 < x < 6$.

Lastly, let's pick $x = 7$ (a value greater than 6): $x^2 - 5x - 6 = 7^2 - 5(7) - 6 = 49 - 35 - 6 = 8 > 0$

The expression is positive (+) for $x > 6$.

Step 4: Combine the intervals based on the signs from the sign chart: Since the inequality is $x^2 - 5x - 6 < 0$, we are looking for the intervals where the expression is negative (-).

The solution is: $-1 < x < 6$.

So, the solution to the inequality is $x$ belongs to the open interval $(-1, 6)$.