Question

Квадратные уравнения. 2х^2+3х-5=0; 5х^2-7х+2=0; 3х^2+5х-2=0; 2х^2-7х+3=0; Помоги решить,срочно! Пожалуйста

Answer 1

1) по свойству а+в+с=0
х1=1, х2=-5/2=-2,5
2)по свойству а+в+с=0
х1=1, х2=2/5=0,4
3 и 4 во вложении

Answer 2

Quadratic Equations

Sure, I can help you with solving these quadratic equations. Let's solve each of them step by step.

1. 2x^2 + 3x - 5 = 0: - To solve this equation, we can use the quadratic formula: \[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\] - Here, a = 2, b = 3, and c = -5. - Plugging these values into the quadratic formula, we get: \[x = \frac{{-3 \pm \sqrt{{3^2 - 4*2*(-5)}}}}{{2*2}}\] - Solving for x gives us two solutions: \[x = \frac{{-3 + \sqrt{49}}}{{4}} = \frac{{-3 + 7}}{{4}} = 1\] \[x = \frac{{-3 - \sqrt{49}}}{{4}} = \frac{{-3 - 7}}{{4}} = -2.5\] - So, the solutions for the equation 2x^2 + 3x - 5 = 0 are x = 1 and x = -2.5.

2. 5x^2 - 7x + 2 = 0: - Using the quadratic formula again, with a = 5, b = -7, and c = 2: \[x = \frac{{7 \pm \sqrt{{(-7)^2 - 4*5*2}}}}{{2*5}}\] - Solving for x gives us: \[x = \frac{{7 + \sqrt{49 - 40}}}{{10}} = \frac{{7 + 3}}{{10}} = 1\] \[x = \frac{{7 - \sqrt{49 - 40}}}{{10}} = \frac{{7 - 3}}{{10}} = 0.4\] - Therefore, the solutions for the equation 5x^2 - 7x + 2 = 0 are x = 1 and x = 0.4.

3. 3x^2 + 5x - 2 = 0: - Once again, using the quadratic formula with a = 3, b = 5, and c = -2: \[x = \frac{{-5 \pm \sqrt{{5^2 - 4*3*(-2)}}}}{{2*3}}\] - Solving for x gives us: \[x = \frac{{-5 + \sqrt{25 + 24}}}{{6}} = \frac{{-5 + 7}}{{6}} = \frac{1}{3}\] \[x = \frac{{-5 - \sqrt{25 + 24}}}{{6}} = \frac{{-5 - 7}}{{6}} = -2\] - Hence, the solutions for the equation 3x^2 + 5x - 2 = 0 are x = 1/3 and x = -2.

4. 2x^2 - 7x + 3 = 0: - Using the quadratic formula with a = 2, b = -7, and c = 3: \[x = \frac{{7 \pm \sqrt{{(-7)^2 - 4*2*3}}}}{{2*2}}\] - Solving for x gives us: \[x = \frac{{7 + \sqrt{49 - 24}}}{{4}} = \frac{{7 + 5}}{{4}} = 3\] \[x = \frac{{7 - \sqrt{49 - 24}}}{{4}} = \frac{{7 - 5}}{{4}} = 0.5\] - Therefore, the solutions for the equation 2x^2 - 7x + 3 = 0 are x = 3 and x = 0.5.

I hope this helps! Let me know if you have any other questions.