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
Anvisha [2.4K]
2 years ago
15

Find all real solutions to the equation (x² − 6x +3)(2x² − 4x − 7) = 0.

Mathematics
1 answer:
Jet001 [13]2 years ago
7 0

Answer:

x = 3 + √6 ; x = 3 - √6 ; x = \frac{2+3\sqrt{2}}{2} ;  x = \frac{2-(3)\sqrt{2}}{2}

Step-by-step explanation:

Relation given in the question:

(x² − 6x +3)(2x² − 4x − 7) = 0

Now,

for the above relation to be true the  following condition must be followed:

Either  (x² − 6x +3) = 0 ............(1)

or

(2x² − 4x − 7) = 0 ..........(2)

now considering the equation (1)

(x² − 6x +3) = 0

the roots can be found out as:

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

for the equation ax² + bx + c = 0

thus,

the roots are

x = \frac{-(-6)\pm\sqrt{(-6)^2-4\times1\times(3)}}{2\times(1)}

or

x = \frac{6\pm\sqrt{36-12}}{2}

or

x = \frac{6+\sqrt{24}}{2} and, x = x = \frac{6-\sqrt{24}}{2}

or

x = \frac{6+2\sqrt{6}}{2} and, x = x = \frac{6-2\sqrt{6}}{2}

or

x = 3 + √6 and x = 3 - √6

similarly for (2x² − 4x − 7) = 0.

we have

the roots are

x = \frac{-(-4)\pm\sqrt{(-4)^2-4\times2\times(-7)}}{2\times(2)}

or

x = \frac{4\pm\sqrt{16+56}}{4}

or

x = \frac{4+\sqrt{72}}{4} and, x = x = \frac{4-\sqrt{72}}{4}

or

x = \frac{4+\sqrt{2^2\times3^2\times2}}{2} and, x = x = \frac{4-\sqrt{2^2\times3^2\times2}}{4}

or

x = \frac{4+(2\times3)\sqrt{2}}{2} and, x = x = \frac{4-(2\times3)\sqrt{2}}{4}

or

x = \frac{2+3\sqrt{2}}{2} and, x = \frac{2-(3)\sqrt{2}}{2}

Hence, the possible roots are

x = 3 + √6 ; x = 3 - √6 ; x = \frac{2+3\sqrt{2}}{2} ; x = \frac{2-(3)\sqrt{2}}{2}

You might be interested in
Order of Operations
Rufina [12.5K]

9 - (a - 7)

Note that - = -1

First, distribute - 1 to all terms within the parenthesis

-1(a - 7) = -a + 7

9 - a + 7

Combine like terms

9 + 7 = 16

-a + 16, or A. 16 - a is your answer

hope this helps

8 0
2 years ago
Read 2 more answers
According to the Venn diagram what type of parallelogram is both a rectangle and a rhombus
Brut [27]
A square can be both a rectangle and a rhombus
4 0
3 years ago
Read 2 more answers
Someone pls help me I will make you brain
Sergio039 [100]
The answer is the 2nd choice, number of sales.

The function described f(x) = B + Cx
5 0
2 years ago
PLEASE HELP ME<br> Find the total surface area of the figure shown.
otez555 [7]

Answer:

I think it's C but I might be

Step-by-step explanation:

8 0
2 years ago
F (x) = -3x + 2x – 5 Whatisf (-1)?​
eduard

Answer:

f(-1) = -4

Step-by-step explanation:

f(-1) simply means that what is f(x) when x = -1?

Just plug in -1 for <em>x</em> to find your answer:

f(-1) = -3(-1) + 2(-1) - 5

f(-1) = 3 - 2 - 5

f(-1) = 1 - 5

f(-1) = -4

7 0
3 years ago
Other questions:
  • A triangle has an area of 54 m 2 2 and a height of 9 m. How long is the base of the triangle? Enter your answer in the box.
    5·1 answer
  • A man at the shopping plaza is standing 50 meters from AD, and 40 meters from DC,
    8·1 answer
  • What is the scale of the map if 1 cm on the map represents 20km in reallife
    15·1 answer
  • Factor 2x^2+4x+18 !!!!!
    8·2 answers
  • Please help Carlos has a monthly budget of $250.00 for clothing. He spent $61.96 the first week, $52.43 the second week, and $72
    10·1 answer
  • The mean waiting time at the drive-through of a fast-food restaurant from the time the food is ordered to when it is received is
    12·1 answer
  • An equation that detemine the center, the radius, and one point of the circle​
    11·1 answer
  • For the multiple regression model Y with hat on top equals 40 plus 15 X subscript 1 minus 10 X subscript 2 plus 5 X subscript 3,
    11·1 answer
  • HELP PLEASE! Write a quadratic function that passes through the point (-1,9), has an axis of symmetry of x=-3 and a minimum valu
    7·1 answer
  • Find the length of an altitude of an equilateral triangle with sides of 4 cm.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!