Question

1) 3х^2-4-24=0 2) 4=20x-25x^2 3)-25=10x+x^2

Answer 1

2)4=20x-25x^2
25x^2-20x+4=0
D=400-4*25*4=400-400=0
D=0
x=-b/2a
x=20/50
x=0,4

3)-25=10x+x^2
x^2+10x+25=0
D=100-4*25=100-100=0
D=0
x=-10/2
x=-5

Answer 2

To solve these quadratic equations, let's work on them one by one:

1. 3x^2 - 4x - 24 = 0

To solve this equation, we can use the quadratic formula, which states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -4, and c = -24. Substituting these values into the quadratic formula, we have:

x = (-(-4) ± √((-4)^2 - 4 * 3 * (-24))) / (2 * 3) x = (4 ± √(16 + 288)) / 6 x = (4 ± √304) / 6

So the solutions to the equation are:

x = (4 + √304) / 6 x = (4 - √304) / 6

2. 4 = 20x - 25x^2

To solve this equation, we rearrange it to the standard form:

25x^2 - 20x + 4 = 0

Now, let's use the quadratic formula with a = 25, b = -20, and c = 4:

x = (-(-20) ± √((-20)^2 - 4 * 25 * 4)) / (2 * 25) x = (20 ± √(400 - 400)) / 50 x = (20 ± √0) / 50

Since the discriminant (√(400 - 400)) is zero, the equation has only one solution:

x = 20 / 50 x = 2 / 5 x = 0.4

3. -25 = 10x + x^2

Rearranging the equation:

x^2 + 10x + 25 = 0

Using the quadratic formula with a = 1, b = 10, and c = 25:

x = (-10 ± √(10^2 - 4 * 1 * 25)) / (2 * 1) x = (-10 ± √(100 - 100)) / 2 x = (-10 ± √0) / 2

Again, since the discriminant is zero, the equation has only one solution:

x = -10 / 2 x = -5