Question

При яких значеннях a рівняння не має коренів​

Answer 1

Ответ: 1,125

$(a - 1)x^{2} + (2a - 3)x + a = 0$

$D = {(2a - 3)}^{2} - 4(a - 1)a = {4a}^{2} - 12a + 9 - {4a}^{2} + 4a = - 8a + 9$

Уравнение не имеет значения когда тогда Дискриминант меньше нуля

$- 8a + 9 < 0 \\ - 8a < - 9 \\ a > \frac{9}{8} = 1.125$

Answer 2

When does the equation have no roots?

An equation does not have any roots when the discriminant is negative. The discriminant is the expression inside the square root in the quadratic formula, which is used to find the roots of a quadratic equation.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Where a, b, and c are the coefficients of the quadratic equation in the form of ax^2 + bx + c = 0.

If the discriminant (b^2 - 4ac) is negative, then the equation has no real roots. This means that the graph of the quadratic equation does not intersect the x-axis, and there are no values of x that satisfy the equation.

Let's consider an example to illustrate this:

Example: Consider the quadratic equation 2x^2 + 3x + 4 = 0.

Using the quadratic formula, we can find the discriminant:

Discriminant = b^2 - 4ac = (3^2) - 4(2)(4) = 9 - 32 = -23

Since the discriminant is negative (-23), the equation 2x^2 + 3x + 4 = 0 has no real roots.

Therefore, when the discriminant is negative, the quadratic equation does not have any roots.