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Liono4ka [1.6K]
3 years ago
13

What are the solutions of x^2-2x+5=0

Mathematics
1 answer:
sweet [91]3 years ago
6 0

The solution of x^{2}-2 x+5=0 are 1 + 2i and 1 – 2i

<u>Solution:</u>

Given, equation is x^{2}-2 x+5=0

We have to find the roots of the given quadratic equation

Now, let us use the quadratic formula

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}  --- (1)

<em><u>Let us determine the nature of roots:</u></em>

Here in x^{2}-2 x+5=0 a = 1 ; b = -2 ; c = 5

b^2 - 4ac = 2^2 - 4(1)(5) = 4 - 20 = -16

Since b^2 - 4ac < 0 , the roots obtained will be complex conjugates.

Now plug in values in eqn 1, we get,

x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4 \times 1 \times 5}}{2 \times 1}

On solving we get,

x=\frac{2 \pm \sqrt{4-20}}{2}

x=\frac{2 \pm \sqrt{-16}}{2}

x=\frac{2 \pm \sqrt{16} \times \sqrt{-1}}{2}

we know that square root of -1 is "i" which is a complex number

\begin{array}{l}{\mathrm{x}=\frac{2 \pm 4 i}{2}} \\\\ {\mathrm{x}=1 \pm 2 i}\end{array}

Hence, the roots of the given quadratic equation are 1 + 2i and 1 – 2i

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Answer:

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<u>or</u>

<u>f(x)=5x+7</u>

Step-by-step explanation:

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Using the equation y=mx+b, you can find m and b to make y=5x+7.

Steps:

(1, 12) (2, 17)                          formula: y2-y1 / x2-x1 = m

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<u>or</u>

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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This means that n = 40, s = \frac{20.2}{\sqrt{40}}

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By the Central Limit Theorem

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0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

Z = \frac{X - \mu}{s}

Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = -0.22

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Niccherip5 and 19 more users found this answer helpful

THANKS

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