Question

При каких значениях к число 3 находится между корнями уровнения Х в квадрате +х+(к-1)(к+7)

Answer 1

Ответ: при -5<k<-1
.....

Answer 2

Equation Analysis

The given equation is: x^2 - x(k-1)(k+7).

To find the values of k for which the number 3 lies between the roots of the equation, we can use the discriminant of the quadratic equation.

The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by the formula: D = b^2 - 4ac.

If the discriminant is greater than 0, the equation has two distinct real roots. If the discriminant is equal to 0, the equation has two equal real roots. If the discriminant is less than 0, the equation has no real roots.

Calculation of Discriminant

For the given equation x^2 - x(k-1)(k+7), the coefficients are: - a = 1 - b = -k(k+6) - c = 0

The discriminant (D) is given by: D = (-k(k+6))^2 - 4*1*0.

Finding the Range of k

To find the range of values for k for which the number 3 lies between the roots of the equation, we need to solve the inequality obtained from the discriminant being greater than 0.

Let's calculate the discriminant and solve for the range of k.