Question

A)2x^2-5x+2=0 B)3x^2+10x+3=0 C)4x^2+5x-6=0 D)3x^2-x-2=0

Answer 1

А) х 1=2; х2= 0,5
B)x1= -1\3; x2= -3
C)x1=9\4; Х2=-1
D)х1=1; х2=-2/3

Answer 2

A) 2x^2 - 5x + 2 = 0:

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

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 2, b = -5, and c = 2. Substituting these values into the quadratic formula:

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

So, the two solutions are x = (5 + 3) / 4 = 2 and x = (5 - 3) / 4 = 1/2.

Therefore, the solutions to the equation 2x^2 - 5x + 2 = 0 are x = 2 and x = 1/2.

B) 3x^2 + 10x + 3 = 0:

Using the quadratic formula again, we can find the solutions for this equation. Here, a = 3, b = 10, and c = 3.

x = (-10 ± √(10^2 - 4 * 3 * 3)) / (2 * 3) = (-10 ± √(100 - 36)) / 6 = (-10 ± √64) / 6 = (-10 ± 8) / 6

So, the two solutions are x = (-10 + 8) / 6 = -1/3 and x = (-10 - 8) / 6 = -3.

Therefore, the solutions to the equation 3x^2 + 10x + 3 = 0 are x = -1/3 and x = -3.

C) 4x^2 + 5x - 6 = 0:

For this equation, a = 4, b = 5, and c = -6.

x = (-5 ± √(5^2 - 4 * 4 * -6)) / (2 * 4) = (-5 ± √(25 + 96)) / 8 = (-5 ± √121) / 8 = (-5 ± 11) / 8

So, the two solutions are x = (-5 + 11) / 8 = 3/4 and x = (-5 - 11) / 8 = -2.

Therefore, the solutions to the equation 4x^2 + 5x - 6 = 0 are x = 3/4 and x = -2.

D) 3x^2 - x - 2 = 0:

In this equation, a = 3, b = -1, and c = -2.

x = (-(-1) ± √((-1)^2 - 4 * 3 * -2)) / (2 * 3) = (1 ± √(1 + 24)) / 6 = (1 ± √25) / 6 = (1 ± 5) / 6

So, the two solutions are x = (1 + 5) / 6 = 1 and x = (1 - 5) / 6 = -2/3.

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

To summarize: A) 2x^2 - 5x + 2 = 0 has solutions x = 2 and x = 1/2. B) 3x^2 + 10x + 3 = 0 has solutions x = -1/3 and x = -3. C) 4x^2 + 5x - 6 = 0 has solutions x = 3/4 and x = -2. D) 3x^2 - x - 2 = 0 has solutions x = 1 and x = -2/3.