Question

При якому значенні параметра а рівняння ах + 1 = 3х + а не має коренів?

Answer 1

Ax + 1 = 3x + a
ax - 3x = a - 1
x(a - 3) = a - 1
При а = 3 левая часть = 0, а правая нет, значит корней нет.

Answer 2

Understanding the Parameter "a" in the Equation "ax^2 + 1 = 3x"

The given equation is ax^2 + 1 = 3x. To understand under what conditions this equation has no roots, we need to consider the discriminant of the quadratic equation.

Discriminant of a Quadratic Equation

The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the formula Δ = b^2 - 4ac. The discriminant determines the nature of the roots of the quadratic equation.

Conditions for No Roots

For the given equation ax^2 + 1 = 3x, the discriminant is Δ = (-3)^2 - 4a(1), which simplifies to Δ = 9 - 4a.

The equation will have no real roots if the discriminant is negative, i.e., Δ < 0. Therefore, for the given equation to have no roots, the discriminant Δ must be less than zero.

Conclusion

In conclusion, the equation ax^2 + 1 = 3x will have no roots when the discriminant Δ = 9 - 4a is less than zero, i.e., 9 - 4a < 0.

Let's verify this conclusion with the search results.