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
Construct a triangle whose sides are 3 in., 1 1/2 in., 2 3/8 in., 2 in., 3 1/2 in.
Luda [366]
That's 5 lengths for a three sided shape... Are you sure that is the instructions?
6 0
3 years ago
Defining What are the expressed powers and implied<br> powers of the national government?
Marizza181 [45]

Answer:

Constitution has given each separate system of government specific powers. There are three types of Delegated powers

Step-by-step explanation:

4 0
3 years ago
3) 9i(3)+ 9i(2)+ 18i + 36​
GalinKa [24]
Answer:
36+63i




explanation:








7 0
3 years ago
What is the slope of a line parallel to the line containing (-6,1) and (3,-2)
timama [110]

Answer:

m = -\frac{3}{9}

Step-by-step explanation:

Use the following formula:

slope: m = (y_{2} - y_{1})/(x_{2} - x_{1})

Let:

(x_{1} , y_{1}) = (-6 , 1)\\ (x_{2} , y_ {2}) = (3 , -2)\\

Plug in the corresponding numbers to the corresponding variables:

m = \frac{-2 - 1}{3 - (-6)}\\\\m = \frac{-3}{3 + 6}\\\\m = \frac{-3}{9}

m = -\frac{3}{9} is your answer.

~

3 0
3 years ago
5x+8=28<br> Solve it because I don’t get it
Soloha48 [4]

Answer:

28 - 8= 20 ÷ 5 = 4

Step-by-step explanation:

Use distributive property. The answer is 4

4 0
3 years ago
Read 2 more answers
Other questions:
  • -6.56 × 14.2 = !!!!!
    11·1 answer
  • A luncheon for 36 guests costs $207. what was the cost per guest?
    14·2 answers
  • Enter the sum of the numbers as the product of their GCF and another sum. 42 + 30
    10·2 answers
  • How long will it take for a $3000 savings account to double its value at a simple interest rate of 10%?
    13·1 answer
  • P(4 and C) I need help asap
    7·1 answer
  • How does multiplying powers with the same base from multiplying powers with the same exponent but different bases
    6·2 answers
  • How much would you pay for 5 apples at the rate of $6.60 a dozen?
    11·2 answers
  • Which equations represent linear functions? Select all that apply.
    5·1 answer
  • 15 ft above sea level
    6·1 answer
  • two angles of a triangle measure 59 degrees and 63 degrees. if the longest side measures 28 cm find the length of the shortest s
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!