It seems like there's a bit of confusion in your question as it's not clear what you're asking. However, I'll try to address the parts that I can.

The quadratic equation is given as x² - 2x + μ = 0. The roots of a quadratic equation ax² + bx + c = 0 are given by the formula x = [-b ± sqrt(b² - 4ac)] / 2a.

In this case, a = 1, b = -2, and c = μ. So the roots are x = [2 ± sqrt((2)² - 4*1*μ)] / 2*1 = [2 ± sqrt(4 - 4μ)] / 2.

The difference between the roots is given as 2. So, 2 = sqrt(4 - 4μ) - (-sqrt(4 - 4μ)) = 2sqrt(4 - 4μ).

Squaring both sides to eliminate the square root gives 4 = 4(4 - 4μ). Simplifying gives 1 = 4 - 4μ, and solving for μ gives μ = 3/4.

The relation between 2 and μ is not clear from your question. If you meant to ask for the relation between 2 and u, it's also not clear as there's no variable u in the given equation.

The equations involving λ are also not clear as there's no variable λ in the original equation. If you could provide more context or clarify your question, I'd be happy to help further!

Question

It seems like there's a bit of confusion in your question as it's not clear what you're asking. However, I'll try to address the parts that I can.

The quadratic equation is given as x² - 2x + μ = 0. The roots of a quadratic equation ax² + bx + c = 0 are given by the formula x = [-b ± sqrt(b² - 4ac)] / 2a.

In this case, a = 1, b = -2, and c = μ. So the roots are x = [2 ± sqrt((2)² - 4*1*μ)] / 2*1 = [2 ± sqrt(4 - 4μ)] / 2.

The difference between the roots is given as 2. So, 2 = sqrt(4 - 4μ) - (-sqrt(4 - 4μ)) = 2sqrt(4 - 4μ).

Squaring both sides to eliminate the square root gives 4 = 4(4 - 4μ). Simplifying gives 1 = 4 - 4μ, and solving for μ gives μ = 3/4.

The relation between 2 and μ is not clear from your question. If you meant to ask for the relation between 2 and u, it's also not clear as there's no variable u in the given equation.

The equations involving λ are also not clear as there's no variable λ in the original equation. If you could provide more context or clarify your question, I'd be happy to help further!

Knowee AI · Accepted Answer

It seems like there's a bit of confusion in your question as it's not clear what you're asking. However, I'll try to address the parts that I can.

The quadratic equation is given as x² - 2x + μ = 0. The roots of a quadratic equation ax² + bx + c = 0 are given by the formula x = [-b ± sqrt(b² - 4ac)] / 2a.

In this case, a = 1, b = -2, and c = μ. So the roots are x = [2 ± sqrt((2)² - 4*1*μ)] / 2*1 = [2 ± sqrt(4 - 4μ)] / 2.

The difference between the roots is given as 2. So, 2 = sqrt(4 - 4μ) - (-sqrt(4 - 4μ)) = 2sqrt(4 - 4μ).

Squaring both sides to eliminate the square root gives 4 = 4(4 - 4μ). Simplifying gives 1 = 4 - 4μ, and solving for μ gives μ = 3/4.

The relation between 2 and μ is not clear from your question. If you meant to ask for the relation between 2 and u, it's also not clear as there's no variable u in the given equation.

The equations involving λ are also not clear as there's no variable λ in the original equation. If you could provide more context or clarify your question, I'd be happy to help further!

If the difference between the roots of x²-2x+μ=0 is 2, then the relation between 2 and u is___________λ = 4(μ + 1)λ² =(μ + 1)λ = 4(μ + 1)²λ² = 4(μ + 1)

Question

If the difference between the roots of $x² - 2x + \mu = 0$ is 2, then the relation between 2 and $u$ is___________\n $\lambda = 4(\mu + 1)$ \n $\lambda² = (\mu + 1)$ \n $\lambda = 4(\mu + 1)²$ \n $\lambda² = 4(\mu + 1)$

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