Question

7х^2-31х-6=0 решите пример дискриминантом

Answer 1

D= b^2 - 4*a*c=(-31)^2 - 4*(-6)*7= 961 + 168= 1129
x=(-b±√d)/2a = (31±√1129)/14

Answer 2

7х²-31х-6=0
D=b²-4ca=(-31)²-4*7*(-6)=961+168=1129
x1=31-√1129 \ 14
x2=31+√1129\14

Answer 3

Solving the Quadratic Equation Using the Discriminant

To solve the quadratic equation 7x^2 - 31x - 6 = 0 using the discriminant, we can use the quadratic formula, which is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Where: - a is the coefficient of x^2, - b is the coefficient of x, and - c is the constant term.

Calculating the Discriminant

The discriminant, denoted by Δ (delta), is calculated using the formula:

Δ = b^2 - 4ac

Applying the Quadratic Formula

Let's first calculate the discriminant and then use it to solve the given quadratic equation.

Calculating the Discriminant for the Given Equation

For the equation 7x^2 - 31x - 6 = 0: - a = 7 - b = -31 - c = -6

Using the formula Δ = b^2 - 4ac, we can calculate the discriminant:

Δ = (-31)^2 - 4 * 7 * (-6)

Δ = 961 + 168

Δ = 1129

Using the Discriminant to Solve the Equation

Now that we have calculated the discriminant Δ = 1129, we can use it to find the solutions for the given quadratic equation.

The solutions are given by the quadratic formula:

x = (-b ± √Δ) / (2a)

Substituting the values of a, b, and Δ into the quadratic formula, we get:

x = (31 ± √1129) / 14

So, the solutions for the given quadratic equation 7x^2 - 31x - 6 = 0 using the discriminant are:

x = (31 + √1129) / 14 and x = (31 - √1129) / 14