Question

Определите знаки корней уравнения (если корни существуют): 5х^2 -x+1=0

Answer 1

5x^2-x+1=0, D=1-4*5*1<0, корней нет.

Answer 2

$5x^2-x+1=0\\D=b^2-4ac=(-1)^2-4*5*1=1-20=-19\ \textless \ 0$

Ответ: корней нет.

Answer 3

The question is to determine the signs of the roots of the equation (if the roots exist): 5x^2 - x + 1 = 0. To do this, we need to find the discriminant of the equation, which is D = b^2 - 4ac, where a = 5, b = -1, and c = 1. Plugging these values into the formula, we get D = (-1)^2 - 4(5)(1) = 1 - 20 = -19. Since the discriminant is negative, the equation has no real roots, and therefore the question of their signs is meaningless. However, if we consider complex roots, then we can use the formula x = (-b ± √D) / (2a) to find them. In this case, we get x = (1 ± √(-19)) / 10, which can be written as x = (1 ± i√19) / 10, where i is the imaginary unit. The complex roots have both real and imaginary parts, and their signs depend on the sign of the imaginary part. The root x = (1 + i√19) / 10 has a positive imaginary part, and therefore it is considered to have a positive sign. The root x = (1 - i√19) / 10 has a negative imaginary part, and therefore it is considered to have a negative sign. This is one way to answer the question, but it may not be what the question intended. For more information, you can check the web search results that I found for you . I hope this helps.