Question

X^2-2x-3<0...........

Answer 1

Ответ; x первый=3
          x второй =-1

Answer 2

To solve the quadratic inequality x^2 - 2x - 3 < 0, we can use a combination of factoring and the sign of the quadratic expression.

First, let's factor the quadratic expression:

x^2 - 2x - 3 = (x - 3)(x + 1)

Now, we can find the critical points by setting each factor equal to zero:

x - 3 = 0 => x = 3 x + 1 = 0 => x = -1

These critical points divide the number line into three intervals: (-∞, -1), (-1, 3), and (3, +∞).

Next, we test a point within each interval to determine the sign of the quadratic expression:

For x = -2 (within the interval (-∞, -1)): (x - 3)(x + 1) = (-2 - 3)(-2 + 1) = (-5)(-1) = 5 Since 5 > 0, the expression is positive in the interval (-∞, -1).

For x = 0 (within the interval (-1, 3)): (x - 3)(x + 1) = (0 - 3)(0 + 1) = (-3)(1) = -3 Since -3 < 0, the expression is negative in the interval (-1, 3).

For x = 4 (within the interval (3, +∞)): (x - 3)(x + 1) = (4 - 3)(4 + 1) = (1)(5) = 5 Since 5 > 0, the expression is positive in the interval (3, +∞).

From the above analysis, we can conclude that the solution to the inequality x^2 - 2x - 3 < 0 is the interval (-1, 3).

In interval notation, the solution can be written as (-1, 3).