Question

найти корни трехчлена: х²-11х+30; х²-21х+110; 4х²-64; 4х²-2х-0,75 помогите пожалуйста

Answer 1

x^2-11+30=0

D=(-11)^2-4*1*30 = 121-120 = 1

VD = V1 = 1

x1 = (11+1)/2 = 12/2=6

x2 = (11-1)/2 = 10/2 = 5

 

 

x^2-21x+110=0

D=(-21)^2-4*1*110=441 - 440 = 1

VD = 1

x1 = (21+1)/2 = 22/2=11

x2 = (21-1)/2 = 20/2 = 10

 

 

4x^2-64=0

4x^2=64

x^2=64:4

x^2=16  / :V

x=4 i x=-4

 

 

4x^2-2x-0,75=0

D=(-2)^2-4*4*(-0,75) = 4+12 = 16

VD=V16 = 4

x1 = (2+4)/2*4 = 6/8 = 3/4

x2 = (2-4)/2*4 = -2/8 = - 1/4

 

 

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Answer 2

Finding the Roots of the Quadratic Equations

Let's find the roots of the given quadratic equations:

1. Equation: x² - 11x + 30

To find the roots, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For this equation, the coefficients are: a = 1, b = -11, c = 30

Plugging these values into the quadratic formula, we get:

x = (-(-11) ± √((-11)² - 4 * 1 * 30)) / (2 * 1)

Simplifying further:

x = (11 ± √(121 - 120)) / 2

x = (11 ± √1) / 2

x = (11 ± 1) / 2

So, the roots of the equation x² - 11x + 30 are:

x₁ = (11 + 1) / 2 = 6

x₂ = (11 - 1) / 2 = 5

2. Equation: x² - 21x + 110

Using the same quadratic formula, we can find the roots of this equation:

For this equation, the coefficients are: a = 1, b = -21, c = 110

Plugging these values into the quadratic formula, we get:

x = (-(-21) ± √((-21)² - 4 * 1 * 110)) / (2 * 1)

Simplifying further:

x = (21 ± √(441 - 440)) / 2

x = (21 ± √1) / 2

x = (21 ± 1) / 2

So, the roots of the equation x² - 21x + 110 are:

x₁ = (21 + 1) / 2 = 11

x₂ = (21 - 1) / 2 = 10

3. Equation: 4x² - 64

This equation is already in the form of a quadratic equation. To find the roots, we can factor out the common factor of 4:

4x² - 64 = 4(x² - 16)

Now, we have a difference of squares:

4x² - 64 = 4(x - 4)(x + 4)

So, the roots of the equation 4x² - 64 are:

x₁ = 4

x₂ = -4

4. Equation: 4x² - 2x - 0.75

To find the roots of this equation, we can use the quadratic formula:

For this equation, the coefficients are: a = 4, b = -2, c = -0.75

Plugging these values into the quadratic formula, we get:

x = (-(-2) ± √((-2)² - 4 * 4 * (-0.75))) / (2 * 4)

Simplifying further:

x = (2 ± √(4 + 12)) / 8

x = (2 ± √16) / 8

x = (2 ± 4) / 8

So, the roots of the equation 4x² - 2x - 0.75 are:

x₁ = (2 + 4) / 8 = 0.75

x₂ = (2 - 4) / 8 = -0.25

I hope this helps! Let me know if you have any further questions.