Question

6x-x^2-5=0 решить дискрименант

Answer 1

6x-x^2-5=0

D=6^2 - 4*5=16

 

x1= (-6-4)/2=1

x2= (-6+4)/2=5

Answer 2

Solving the Equation

To solve the equation 6x - x^2 - 5 = 0, we can use the quadratic formula or factorization method. Let's use the quadratic formula.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Comparing the given equation with the standard quadratic equation ax^2 + bx + c = 0, we have:

a = -1, b = 6, and c = -5.

Substituting these values into the quadratic formula, we get:

x = (-6 ± √(6^2 - 4(-1)(-5))) / (2(-1))

Simplifying further:

x = (-6 ± √(36 - 20)) / (-2)

x = (-6 ± √16) / (-2)

x = (-6 ± 4) / (-2)

Now, we can find the two possible solutions for x:

x1 = (-6 + 4) / (-2) = -2 / (-2) = 1

x2 = (-6 - 4) / (-2) = -10 / (-2) = 5

Therefore, the solutions to the equation 6x - x^2 - 5 = 0 are x = 1 and x = 5.

Calculating the Discriminant

The discriminant of a quadratic equation is given by the expression b^2 - 4ac. It helps determine the nature of the solutions.

For the equation 6x - x^2 - 5 = 0, the coefficients are a = -1, b = 6, and c = -5.

Substituting these values into the discriminant formula, we get:

D = b^2 - 4ac = (6)^2 - 4(-1)(-5) = 36 - 20 = 16

The discriminant D is equal to 16.

By analyzing the value of the discriminant, we can determine the nature of the solutions:

- If D > 0, there are two distinct real solutions. - If D = 0, there is one real solution (a repeated root). - If D < 0, there are no real solutions (only complex solutions).

In this case, since D = 16 > 0, there are two distinct real solutions, which we found to be x = 1 and x = 5.

Therefore, the discriminant of the equation 6x - x^2 - 5 = 0 is 16.