Question

9х+12х+4=0 2х+3х-11=0 найти дискрименант

Answer 1

9х+12х+4=0
D=b^2-4ac=144-144=0

2x-3x-11=0
D=b^2-4ac=9+88=97

Answer 2

To find the discriminant of a quadratic equation, we need to first identify the coefficients of the quadratic terms. In the given equations, we have:

Equation 1: 9x + 12x + 4 = 0 Equation 2: 2x + 3x - 11 = 0

Let's solve each equation separately and then find the discriminant.

Solving Equation 1:

To solve Equation 1, we combine like terms and set the equation equal to zero:

9x + 12x + 4 = 0

Combining like terms: 21x + 4 = 0

Subtracting 4 from both sides: 21x = -4

Dividing both sides by 21: x = -4/21

Solving Equation 2:

To solve Equation 2, we combine like terms and set the equation equal to zero:

2x + 3x - 11 = 0

Combining like terms: 5x - 11 = 0

Adding 11 to both sides: 5x = 11

Dividing both sides by 5: x = 11/5

Finding the Discriminant:

The discriminant (denoted as Δ) of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula Δ = b^2 - 4ac.

For Equation 1, the coefficients are: a = 9 b = 12 c = 4

Using the formula, we can calculate the discriminant: Δ1 = (12)^2 - 4(9)(4)

For Equation 2, the coefficients are: a = 2 b = 3 c = -11

Using the formula, we can calculate the discriminant: Δ2 = (3)^2 - 4(2)(-11)

Let's calculate the discriminants:

Δ1 = (12)^2 - 4(9)(4) = 144 - 144 = 0 Δ2 = (3)^2 - 4(2)(-11) = 9 + 88 = 97

Therefore, the discriminant for Equation 1 is 0, and the discriminant for Equation 2 is 97.

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