Question

4x²-12x+9=0 2x²-5x+2=0 10x²-6x+9=0 3x²-12x+9=0 6x²+5x+1=0

Answer 1

Ответ:

х=1,5

х₁=2 x₂=0,5

х$\neq$

х₁=3 x₂=1

х₁=$\frac{-1}{3}$ x₂= -0,5

Пошаговое объяснение:

4x²-12x+9=0

D = b²-4ac

D = (-12)²-4*4*9=144-144=0

x = - $\frac{b}{2a}$

x = - $\frac{-12}{2*4}$

x = 1,5

2x²-5x+2=0

D = b²-4ac

D = (-5)²-4*2*2= 25-16=9

х₁=$\frac{-b+\sqrt{D} } {2a}$

х₁=$\frac{5+3}{2*2}$=$\frac{8}{4}$=2

х₂ =$\frac{-b-\sqrt{D} }{2a}$

х₂=$\frac{5-3}{4}$=$\frac{2}{4}$=0,5

10x²-6x+9=0

D = b²-4ac

D = (-6)²-4*9*10=36-360= -324

x$\neq$

3x²-12x+9=0

D = b²-4ac

D = (-12)²-4*9*3=144-108=36

х₁=$\frac{-b+\sqrt{D} } {2a}$

x₁=$\frac{12+6}{2*3}$=$\frac{18}{6}$=3

х₂ =$\frac{-b-\sqrt{D} }{2a}$

x₂=$\frac{12-6}{6}$=1

6x²+5x+1=0

D = b²-4ac

D = 5²-4*1*6=25-24=1

х₁=$\frac{-b+\sqrt{D} } {2a}$

x₁=$\frac{-5+1}{2*6}$=$\frac{-4}{12}$= $\frac{-1}{3}$

х₂ =$\frac{-b-\sqrt{D} }{2a}$

x₂=$\frac{-5-1}{12}$=$\frac{-6}{12}$= -0,5

Answer 2

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

For a quadratic equation of the form ax² + bx + c = 0, the quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

Let's solve each equation one by one:

1. 4x² - 12x + 9 = 0 a = 4, b = -12, c = 9

x = (-(-12) ± √((-12)² - 4 * 4 * 9)) / (2 * 4) x = (12 ± √(144 - 144)) / 8 x = (12 ± √0) / 8 x = (12 ± 0) / 8 x = 12 / 8 x = 3/2

The solution to the first equation is x = 3/2.

2. 2x² - 5x + 2 = 0 a = 2, b = -5, c = 2

x = (-(-5) ± √((-5)² - 4 * 2 * 2)) / (2 * 2) x = (5 ± √(25 - 16)) / 4 x = (5 ± √9) / 4 x = (5 ± 3) / 4

For x = (5 + 3) / 4, x = 8 / 4 = 2 For x = (5 - 3) / 4, x = 2 / 4 = 1/2

The solutions to the second equation are x = 2 and x = 1/2.

3. 10x² - 6x + 9 = 0 a = 10, b = -6, c = 9

x = (-(-6) ± √((-6)² - 4 * 10 * 9)) / (2 * 10) x = (6 ± √(36 - 360)) / 20 x = (6 ± √(-324)) / 20

The solutions involve complex numbers and are not real-valued.

4. 3x² - 12x + 9 = 0 a = 3, b = -12, c = 9

x = (-(-12) ± √((-12)² - 4 * 3 * 9)) / (2 * 3) x = (12 ± √(144 - 108)) / 6 x = (12 ± √36) / 6 x = (12 ± 6) / 6

For x = (12 + 6) / 6, x = 18 / 6 = 3 For x = (12 - 6) / 6, x = 6 / 6 = 1

The solutions to the fourth equation are x = 3 and x = 1.

5. 6x² + 5x + 1 = 0 a = 6, b = 5, c = 1

x = (-(5) ± √(5² - 4 * 6 * 1)) / (2 * 6) x = (-5 ± √(25 - 24)) / 12 x = (-5 ± √1) / 12 x = (-5 ± 1) / 12

For x = (-5 + 1) / 12, x = -4 / 12 = -1/3 For x = (-5 - 1) / 12, x = -6 / 12 = -1/2

The solutions to the fifth equation are x = -1/3 and x = -1/2.