Question

182х²+241х-423=0 дискриминант с объяснением решения​

Answer 1

Ответ:

D=58081+4×182×423=366025=605²

x1=-241+605/364=1

x2=-241-605/364=-2.32

Answer 2

To find the discriminant of the quadratic equation 182x² + 241x - 423 = 0, we can use the formula:

Discriminant (D) = b² - 4ac

In this equation, a = 182, b = 241, and c = -423. Plugging these values into the formula, we get:

D = (241)² - 4 * (182) * (-423)

D = 58081 - (-295584)

D = 58081 + 295584

D = 353665

Therefore, the discriminant of the quadratic equation 182x² + 241x - 423 = 0 is 353665.

The discriminant helps us determine the nature of the roots of a quadratic equation. Here's how it relates to the solutions:

1. If the discriminant (D) is positive (D > 0), then the quadratic equation has two distinct real roots. In this case, the value of D (353665) is positive, indicating that the equation has two real solutions.

2. If the discriminant (D) is zero (D = 0), then the quadratic equation has one real root (a double root).

3. If the discriminant (D) is negative (D < 0), then the quadratic equation has no real roots. Instead, it has a pair of complex conjugate roots.

In your case, since the discriminant (D) is positive, the equation 182x² + 241x - 423 = 0 has two distinct real solutions. To find the values of x, you can use the quadratic formula:

x = (-b ± √D) / (2a)

Plugging in the values from your equation, we have:

x = (-241 ± √353665) / (2 * 182)

This will give you the two solutions for x.