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
Which equation shows a line perpendicular to the line
LenaWriter [7]

Answer:

The second answer: y= 3/4x + 2

Step-by-step explanation:

Subtract 4x to the other side

Divide by 3 to get y by itself

Make the coefficient of the x term the negative reciprocal, for that is the perpendicular slope of the line

3 0
3 years ago
Clare has a set of cubes with a volume of 1 cm³ each. She also has a box with a volume of 24 cm³. Exactly two layers of cubes ca
Damm [24]

Answer:

12 cubes

Step-by-step explanation:

If the total volume of the box is 24 cm³ and the volume of each cube is 1 cm³ then that means that 24 total cubes can fit perfectly inside the box. Since there can only be two layers of cubes then we simply need to divide the total amount of cubes that will fit in the box by 2 to find the number of cubes in each layer...

24 / 2 = 12 cubes

Finally, we can see that each layer within the box will contain 12 cubes

5 0
3 years ago
B) State a valid formula for multiplying out (A + B)(A − B)
Diano4ka-milaya [45]

(A+B)(A-B) = A^2-B^2.

It's equality constant

8 0
3 years ago
A GMC dealer believes that demand for 2005 Envoys will be normally distributed with a mean of 200 and standard deviation of 30.
irina1246 [14]

Answer:

The correct answer to the following question will be "280 units".

Step-by-step explanation:

The given values are:

Mean = 200

Standard deviation = 30

Let's ask that the supplier needs to reach 99.9% of the standard of operation. To reach this quality of operation, she has to preserve an inventory of

Now,

⇒  Mean + 3\times sigma

On putting the values, we get

⇒  200+3\times 30

⇒  200+90

⇒  290 \ units

290 units would then accomplish a level of service of 99.9%.

Half unpurchased units can indeed be purchased at $30000 i.e. no failure. If he requests 300, there will be losses on 5 products that are unsold.

Hence, ordering 280 units seems to be preferable

3 0
3 years ago
Which of the four is it? ​
Anna11 [10]

Answer:

option 1 i believe

Step-by-step explanation:

just worked it out

i hope this is right and helps <3

6 0
3 years ago
Other questions:
  • The area of the rectangle is 24 square inches. How much longer is its length than its width
    10·1 answer
  • I need help with this now! Please help!
    13·1 answer
  • Need help on this as soon as possibke
    10·1 answer
  • What is the square root of -1 ?
    6·1 answer
  • Solve<br> sin 2 theta = 0.8
    13·1 answer
  • What is the antiderivative of 3x/((x-1)^2)
    6·1 answer
  • The truck’s tank is a stainless steel cylinder. Find the surface area of the tank. Round your answer to the nearest hundredth.
    8·1 answer
  • Calculate 48 x 3/8 choose the numbers to complete the equation
    8·2 answers
  • Tell me something funny for brainliest.
    8·1 answer
  • Which one is a function quick
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!