Question

Найдите сумму всех значений параметра а, при которых уравнение +ax-2x-a имеет единственное решение

Answer 1

$x^2+ax-2x-a=0\\ x^2+(a-2)x-a=0\\\\D=(a-2)^2+4a\\\\(a-2)^2+4a=0\\a^2+4=0\\a^2=-4$
нет корней

PS. кв.уравнение имеет один корень, если дискриминант равен нулю

Answer 2

Solving the Equation for Unique Solutions

To find the sum of all values of the parameter "a" for which the equation \(ax - 2x - a\) has a unique solution, we can use the discriminant of the quadratic equation. The discriminant is given by the formula: \(b^2 - 4ac\), where \(ax^2 + bx + c = 0\) is the quadratic equation.

For the equation \(ax - 2x - a\), the discriminant is \(0\) for a unique solution. This means that the discriminant equation \(b^2 - 4ac = 0\) can be used to find the values of "a" for which the given equation has a unique solution.

Finding the Values of "a"

By substituting the values from the given equation into the discriminant formula, we get:

\(b^2 - 4ac = (-2)^2 - 4(a)(-a) = 4 + 4a^2\)

For a unique solution, the discriminant should be equal to 0:

\(4 + 4a^2 = 0\)

Solving for "a", we get:

\(a^2 = -1\)

This equation has no real solutions, which means there are no real values of "a" for which the given equation has a unique solution.

Conclusion: The equation \(ax - 2x - a\) does not have any real values of "a" for which it has a unique solution.