Question

N1 6x²+18x=0N24x²-9=0N3x²-8x+7=0N43x²+5x+6=0

Answer 1

1)

6х²+18х=0

6х*(х+3)=0

х1=0 или х+3=0

х2=-3

2)

4х²-9=0

(2х+3)(2х-3)=0

2х+3=0 или 2х-3=0

2х=-3 или 2х=3

х1=-1,5; х2=1,5

3)

х²-8х+7=0

D=(-8)*(-8)-4*1*7=64-28=36=6²

x1=(-(-8)+6)/(2*1)=(8+6)/2=14/2=7

x2=(-(-8)-6)/(2*1)=(8-6)/2=2/2=1

4)

3x²+5x+6=0

D=5*5-4*3*6=25-72=-47<0

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Answer 2

Let's solve each quadratic equation one by one:

N1: 6x² + 18x = 0

To solve this equation, we can factor out the common factor of x:

x(6x + 18) = 0

Setting each factor equal to zero gives us:

x = 0 (Solution 1) 6x + 18 = 0 6x = -18 x = -3 (Solution 2)

Therefore, the solutions to N1 are x = 0 and x = -3.

N2: 4x² - 9 = 0

This equation is in the form of a difference of squares. We can factor it as follows:

(2x + 3)(2x - 3) = 0

Setting each factor equal to zero gives us:

2x + 3 = 0 2x = -3 x = -3/2 (Solution 1)

2x - 3 = 0 2x = 3 x = 3/2 (Solution 2)

Therefore, the solutions to N2 are x = -3/2 and x = 3/2.

N3: x² - 8x + 7 = 0

To solve this equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For this equation, a = 1, b = -8, and c = 7. Substituting these values into the quadratic formula, we get:

x = (8 ± √((-8)² - 4(1)(7))) / (2(1)) x = (8 ± √(64 - 28)) / 2 x = (8 ± √36) / 2 x = (8 ± 6) / 2

This gives us two possible solutions:

x = (8 + 6) / 2 = 14 / 2 = 7 (Solution 1) x = (8 - 6) / 2 = 2 / 2 = 1 (Solution 2)

Therefore, the solutions to N3 are x = 7 and x = 1.

N4: 3x² + 5x + 6 = 0

Again, we can use the quadratic formula to solve this equation:

x = (-b ± √(b² - 4ac)) / (2a)

For this equation, a = 3, b = 5, and c = 6. Substituting these values into the quadratic formula, we get:

x = (-5 ± √(5² - 4(3)(6))) / (2(3)) x = (-5 ± √(25 - 72)) / 6 x = (-5 ± √(-47)) / 6

Since we have a negative value under the square root, this equation has complex solutions. We can simplify the expression as follows:

x = (-5 ± √47i) / 6

Therefore, the solutions to N4 are x = (-5 + √47i) / 6 and x = (-5 - √47i) / 6, where i represents the imaginary unit.