Question

10x2-11x+3=0 4x2+12x+5=0 5x2-11x+6=0 6x2+5x-6=0 Дискриминант

Answer 1

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Answer 2

Solution for the Equation 10x^2 - 11x + 3 = 0

To find the solutions for the equation 10x^2 - 11x + 3 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation 10x^2 - 11x + 3 = 0, we have a = 10, b = -11, and c = 3. Plugging these values into the quadratic formula, we get:

x = (-(-11) ± √((-11)^2 - 4 * 10 * 3)) / (2 * 10)

Simplifying further:

x = (11 ± √(121 - 120)) / 20

x = (11 ± √1) / 20

Since the discriminant (√(b^2 - 4ac)) is equal to 1, we have two distinct solutions:

x = (11 + 1) / 20 = 12 / 20 = 0.6

x = (11 - 1) / 20 = 10 / 20 = 0.5

Therefore, the solutions for the equation 10x^2 - 11x + 3 = 0 are x = 0.6 and x = 0.5..

Solution for the Equation 4x^2 + 12x + 5 = 0

To find the solutions for the equation 4x^2 + 12x + 5 = 0, we can again use the quadratic formula. For this equation, we have a = 4, b = 12, and c = 5. Plugging these values into the quadratic formula, we get:

x = (-12 ± √(12^2 - 4 * 4 * 5)) / (2 * 4)

Simplifying further:

x = (-12 ± √(144 - 80)) / 8

x = (-12 ± √64) / 8

Since the discriminant (√(b^2 - 4ac)) is equal to 8, we have two distinct solutions:

x = (-12 + 8) / 8 = -4 / 8 = -0.5

x = (-12 - 8) / 8 = -20 / 8 = -2.5

Therefore, the solutions for the equation 4x^2 + 12x + 5 = 0 are x = -0.5 and x = -2.5..

Solution for the Equation 5x^2 - 11x + 6 = 0

For the equation 5x^2 - 11x + 6 = 0, we can once again use the quadratic formula. Here, a = 5, b = -11, and c = 6. Plugging these values into the quadratic formula, we get:

x = (-(-11) ± √((-11)^2 - 4 * 5 * 6)) / (2 * 5)

Simplifying further:

x = (11 ± √(121 - 120)) / 10

x = (11 ± √1) / 10

Since the discriminant (√(b^2 - 4ac)) is equal to 1, we have two distinct solutions:

x = (11 + 1) / 10 = 12 / 10 = 1.2

x = (11 - 1) / 10 = 10 / 10 = 1

Therefore, the solutions for the equation 5x^2 - 11x + 6 = 0 are x = 1.2 and x = 1..

Solution for the Equation 6x^2 + 5x - 6 = 0

For the equation 6x^2 + 5x - 6 = 0, we can use the quadratic formula. Here, a = 6, b = 5, and c = -6. Plugging these values into the quadratic formula, we get:

x = (-5 ± √(5^2 - 4 * 6 * -6)) / (2 * 6)

Simplifying further:

x = (-5 ± √(25 + 144)) / 12

x = (-5 ± √169) / 12

Since the discriminant (√(b^2 - 4ac)) is equal to 13, we have two distinct solutions:

x = (-5 + 13) / 12 = 8 / 12 = 0.67

**x = (-5 - 13) / 12 = -18