1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
What is the range of the function y= e4x?
Ray Of Light [21]

Answer:

Range is y > 0

Step-by-step explanation:

We need to find the range of y = e^4x

The range is defined as a set of values of dependent variable for which the function is defined.

The exponential function of form c. n^x + k has range f(x) > k

in the given function y = e^4x ,k =0

so Range is y > 0

4 0
3 years ago
Read 2 more answers
Ivan has $1098 worth of $12 and $14 stock shares. The number of $14 shares is seven more than
Dafna1 [17]

Answer:

Number of 12$ Shares? 25

Number of 14$ Shares? 57

Step-by-step explanation:

Let x = number of $12 shares.

Let y = number of $14 shares.

"Ivan has $1098 worth of $12 and $14 stock shares."
12x + 14y = 1098

The number of $14 shares is seven more than twice the number of $12 shares.

y = 2x + 7

We have a system of equations.

12x + 14y = 1098

y = 2x + 7

We can use the substitution method since the second equation is already solved for y. Substitute 2x + 7 for y in the first equation.

12x + 14(2x + 7) = 1098

12x + 28x + 98 = 1098

40x = 1000

x = 25

There are 25 $12 shares.

y = 2x + 7 = 2(25) + 7 = 57

There are 57 $14 shares.

Check:

25 × $12 + 57 × $1`4 = $300 + $798 = $1098

The total value is correct, so the answer is correct.

4 0
2 years ago
Question 2 of 10
RideAnS [48]

Answer: 264,615

Step-by-step explanation:apex

5 0
3 years ago
NEED HELP!!! Can someone help me with 5, 7, and 8??? <br> Need this asap!!!<br> THANK YOU!!!
Serjik [45]

Answer:

5) 8/17 = .471

7) 8/17 = .471

8) 15/17 = .88

Step-by-step explanation:

hope that helps

6 0
3 years ago
Read 2 more answers
Pleaseeeee help with 7-12 I’m strugglingggg!!!
bearhunter [10]

Answer:

7-12 is 5

Step-by-step explanation:

First you want to turn this into addition and make 12 it's inverse 7+(-12) now with 7+(-12) it is basically 12-7. 12-7=5 so your answer is 5

5 0
3 years ago
Read 2 more answers
Other questions:
  • The volume of a rectangular prism is 156 cubic centimeters. The base of the prism has an area of 12 square centimeters.
    8·1 answer
  • N/ -3 + 5 &gt; 4 I really need help on this question if you could please show your work on solving this equation
    11·1 answer
  • Will Mark brainiest!!!
    15·2 answers
  • What is the solution? (Look at picture)
    12·1 answer
  • Please help
    7·1 answer
  • 9/10(x+2/3)=4 1/2<br><br> What is x in this equation
    14·1 answer
  • Acceleration, distance, and time problem, please help!
    9·1 answer
  • HELP PLEASE!! MARKING BRAINLEIST
    14·1 answer
  • Multiply (7.7 × 106)(7 × 105). Express the result in scientific notation.
    11·1 answer
  • How much of a radioactive kind of francium will be left after 44 minutes if you start with 2,616 grams and the half-life is 22 m
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!