Question

1. х2 – 13х + 40 = 0 2. 4х2 + 10x — 6 = 03. 2х2 + 10x + 12 = 04. х2 + 3x + 2 = 05. 2х2 – 18 = 0​

Answer 1

Объяснение:

Вроде должно быть понятно

Answer 2

To solve these quadratic equations, we can use the quadratic formula:

For an equation of the form ax^2 + bx + c = 0, the quadratic formula states:

x = (-b ± √(b^2 - 4ac)) / (2a)

Let's solve each of the given equations one by one:

1. x^2 - 13x + 40 = 0 Here, a = 1, b = -13, and c = 40. Using the quadratic formula:

x = (-(-13) ± √((-13)^2 - 4140)) / (2*1) x = (13 ± √(169 - 160)) / 2 x = (13 ± √9) / 2 x = (13 ± 3) / 2

So, the solutions are: x1 = (13 + 3) / 2 = 16/2 = 8 x2 = (13 - 3) / 2 = 10/2 = 5

Therefore, the solutions to the equation x^2 - 13x + 40 = 0 are x = 8 and x = 5.

2. 4x^2 + 10x - 6 = 0 Here, a = 4, b = 10, and c = -6. Using the quadratic formula:

x = (-(10) ± √((10)^2 - 44(-6))) / (2*4) x = (-10 ± √(100 + 96)) / 8 x = (-10 ± √196) / 8 x = (-10 ± 14) / 8

So, the solutions are: x1 = (-10 + 14) / 8 = 4/8 = 1/2 = 0.5 x2 = (-10 - 14) / 8 = -24/8 = -3

Therefore, the solutions to the equation 4x^2 + 10x - 6 = 0 are x = 0.5 and x = -3.

3. 2x^2 + 10x + 12 = 0 Here, a = 2, b = 10, and c = 12. Using the quadratic formula:

x = (-(10) ± √((10)^2 - 4212)) / (2*2) x = (-10 ± √(100 - 96)) / 4 x = (-10 ± √4) / 4 x = (-10 ± 2) / 4

So, the solutions are: x1 = (-10 + 2) / 4 = -8/4 = -2 x2 = (-10 - 2) / 4 = -12/4 = -3

Therefore, the solutions to the equation 2x^2 + 10x + 12 = 0 are x = -2 and x = -3.

4. x^2 + 3x + 2 = 0 Here, a = 1, b = 3, and c = 2. Using the quadratic formula:

x = (-(3) ± √((3)^2 - 412)) / (2*1) x = (-3 ± √(9 - 8)) / 2 x = (-3 ± √1) / 2 x = (-3 ± 1) / 2

So, the solutions are: x1 = (-3 + 1) / 2 = -2/2 = -1 x2 = (-3 - 1) / 2 = -4/2 = -2

Therefore, the solutions to the equation x^2 + 3x + 2 = 0 are x = -1 and x = -2.

5. 2x^2 - 18 = 0 Here, a = 2, b = 0 (since there's no x term), and c = -18. Using the quadratic formula:

x = (-(0) ± √((0)^2 - 42(-18))) / (2*2) x = (0 ± √(0 + 144)) / 4 x = (0 ± √144) / 4 x = (0 ± 12) / 4

So, the solutions are: x1 = (0 + 12) / 4 = 12/4 = 3 x2 = (0 - 12) / 4 = -12/4 = -3

Therefore, the solutions to the equation 2x^2 - 18 = 0 are x = 3 and x = -3.