Question

1)5X²+4X-1=0 2)16X²-2X-5=0 3)28X²-36+11=0 4)-49X²21X-2=0

Answer 1

1) D=4²-4*5*(-1)=36>0 2 корня
х1=-4+6/2*5=2/10=1/5=0,2
х2=-4-6/2*5=-1
2) D=(-2)²-4*16*(-5)=324>0 2корня
х1=-(-2)+18/2*16=5/8
х2=-(-2)-18/2*16=-1/2=-0,5
3)D=(-36)²-4*28*11=64
x1=36+8/2*28=11/14
x2=36-8/2*28=0,5
4)там после х² какой знак?

Answer 2

Let's solve each quadratic equation one by one:

1. 5X² + 4X - 1 = 0

To solve this equation, we can use the quadratic formula: X = (-b ± √(b² - 4ac)) / (2a).

For this equation, a = 5, b = 4, and c = -1. Plugging these values into the quadratic formula:

X = (-4 ± √(4² - 4 * 5 * -1)) / (2 * 5) X = (-4 ± √(16 + 20)) / 10 X = (-4 ± √36) / 10 X = (-4 ± 6) / 10

We have two solutions: X₁ = (-4 + 6) / 10 = 2 / 10 = 0.2 X₂ = (-4 - 6) / 10 = -10 / 10 = -1

Therefore, the solutions to the equation 5X² + 4X - 1 = 0 are X = 0.2 and X = -1.

2. 16X² - 2X - 5 = 0

Using the quadratic formula again, we can find the solutions for this equation. For this equation, a = 16, b = -2, and c = -5. Plugging these values into the quadratic formula:

X = (-(-2) ± √((-2)² - 4 * 16 * -5)) / (2 * 16) X = (2 ± √(4 + 320)) / 32 X = (2 ± √324) / 32 X = (2 ± 18) / 32

We have two solutions: X₁ = (2 + 18) / 32 = 20 / 32 = 0.625 X₂ = (2 - 18) / 32 = -16 / 32 = -0.5

Therefore, the solutions to the equation 16X² - 2X - 5 = 0 are X = 0.625 and X = -0.5.

3. 28X² - 36 + 11 = 0

Simplifying the equation:

28X² - 25 = 0

To solve this equation, we'll isolate X by moving the constant term to the other side:

28X² = 25

Dividing both sides by 28:

X² = 25/28

Taking the square root of both sides:

X = ±√(25/28)

Since 25/28 is a positive value, we have two solutions:

X₁ = √(25/28) X₂ = -√(25/28)

4. -49X² + 21X - 2 = 0

For this equation, we can again use the quadratic formula to find the solutions. Here, a = -49, b = 21, and c = -2.

X = (-21 ± √(21² - 4 * (-49) * (-2))) / (2 * (-49)) X = (-21 ± √(441 - 392)) / (-98) X = (-21 ± √49) / (-98) X = (-21 ± 7) / (-98)

We have two solutions: X₁ = (-21 + 7) / (-98) = -14 / (-98) = 0.1429 (approximately) X₂ = (-21 - 7) / (-98) = -28 / (-98)