Question

1) 5х^2+2х=02) 6х^2+7х-3=03) 5х^2-10х+17=0

Answer 1

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Answer 2

You've provided three quadratic equations. To solve these equations for the variable "x," you can use the quadratic formula:

For a quadratic equation in the form of ax^2 + bx + c = 0, the quadratic formula is:

x = (-b ± √(b² - 4ac)) / (2a)

Let's solve each of the equations you provided using this formula:

1. 5x^2 + 2x = 0

Here, a = 5, b = 2, and c = 0:

x = (-2 ± √(2² - 4 * 5 * 0)) / (2 * 5) x = (-2 ± √(4)) / 10 x = (-2 ± 2) / 10

This gives us two solutions:

x1 = (-2 + 2) / 10 = 0 / 10 = 0 x2 = (-2 - 2) / 10 = -4 / 10 = -2/5

So, the solutions for this equation are x = 0 and x = -2/5.

2. 6x^2 + 7x - 3 = 0

Here, a = 6, b = 7, and c = -3:

x = (-7 ± √(7² - 4 * 6 * (-3))) / (2 * 6) x = (-7 ± √(49 + 72)) / 12 x = (-7 ± √121) / 12 x = (-7 ± 11) / 12

This gives us two solutions:

x1 = (-7 + 11) / 12 = 4 / 12 = 1/3 x2 = (-7 - 11) / 12 = -18 / 12 = -3/2

So, the solutions for this equation are x = 1/3 and x = -3/2.

3. 5x^2 - 10x + 17 = 0

Here, a = 5, b = -10, and c = 17:

x = (10 ± √((-10)² - 4 * 5 * 17)) / (2 * 5) x = (10 ± √(100 - 340)) / 10 x = (10 ± √(-240)) / 10

Since the discriminant (the value inside the square root) is negative, this equation has complex solutions. Using the complex number "i" for the square root of -1:

x = (10 ± √(240i)) / 10 x = (10 ± √240 * √i) / 10 x = (10 ± 4√15 * i) / 10

Now, we can simplify by dividing everything by 10:

x1 = (10 + 4√15 * i) / 10 = (1 + 2√15 * i) x2 = (10 - 4√15 * i) / 10 = (1 - 2√15 * i)

So, the solutions for this equation are x = 1 + 2√15 * i and x = 1 - 2√15 * i, which are complex numbers.