Question

при каком значении а уравнение ax в квадрате -6x +3=0 имеет только один корень

Answer 1

.................При а=3..................

Answer 2

Solving the Equation for a Single Root

To find the condition under which the equation \(ax^2 - 6x + 3 = 0\) has only one root, we can use the discriminant of the quadratic equation. The discriminant, denoted by \(D\), is given by the formula:

\(D = b^2 - 4ac\)

Where: - \(a\) is the coefficient of \(x^2\) - \(b\) is the coefficient of \(x\) - \(c\) is the constant term

For the equation \(ax^2 - 6x + 3 = 0\), we have: - \(a = a\) - \(b = -6\) - \(c = 3\)

Applying the Discriminant Formula

The discriminant \(D\) determines the nature of the roots of a quadratic equation. If \(D > 0\), the equation has two distinct real roots. If \(D = 0\), the equation has exactly one real root. If \(D < 0\), the equation has no real roots.

Calculating the Discriminant for the Given Equation

Using the formula for the discriminant, we can calculate \(D\) for the given equation:

\(D = (-6)^2 - 4 \cdot a \cdot 3\)

Conclusion

For the equation \(ax^2 - 6x + 3 = 0\) to have only one root, the discriminant \(D\) must be equal to zero.

Therefore, the condition for the equation \(ax^2 - 6x + 3 = 0\) to have only one root is that the discriminant \(D\) equals zero.

[[SOURCE #4]]