Advertisements
Advertisements
Question
Write the following sets in the roaster form:
F = {x | x4 – 5x2 + 6 = 0, x ∈ R}
Advertisements
Solution
Given: F = {x | x4 – 5x2 + 6 = 0, x ∈ R}
To find: Roster form of given set
x4 – 5x2 + 6 = 0
⇒ x4 – 3x2 – 2x2 + 6 = 0
⇒ x2(x2 – 3) – 2(x2 – 3) = 0
⇒ (x2 – 3)(x2 – 2) = 0
⇒ x2 = 3 or 2
⇒ x = `+- sqrt(3)` or `+- sqrt(2)`
⇒ x = `sqrt(3), - sqrt(3), sqrt(2)` or `- sqrt(2)`
So, F = `{- sqrt(3), - sqrt(2), sqrt(2), sqrt(3)}`
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
The collection of all even integers.
Write the following set in roster form:
A = {x : x is an integer and –3 ≤ x < 7}
Write the following set in roster form:
B = {x : x is a natural number less than 6}
Write the following set in the set-builder form:
{3, 6, 9, 12}
Write the following set in the set-builder form:
{5, 25, 125, 625}
List all the elements of the following set:
F = {x : x is a consonant in the English alphabet which precedes k}.
Which of the following collection are sets? Justify your answer:
The collection of all girls in your class.
Which of the following collection is set? Justify your answer:
The collection of ten most talented writers of India.
Which of the following collection are sets? Justify your answer:
A collection of novels written by Munshi Prem Chand.
Describe the following sets in Roster form:
{x ∈ N : x = 2n, n ∈ N};
Describe the following sets in Roster form:
{x : x is a prime number which is a divisor of 60}
Describe the following sets in set-builder form:
E = {0}
List all the elements of the following set:
\[B = \left\{ x: x = \frac{1}{2n - 1}, 1 \leq n \leq 5 \right\}\]
Write the set of all vowels in the English alphabet which precede q.
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \in A\]
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[1 \in A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[2 \subset A\]
Write down all possible proper subsets each of the following set:
{1}.
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
4 _____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
2 _____ A
Describe the following set in Roster form
A = {x/x is a letter of the word 'MOVEMENT'}
Describe the following set in Set-Builder form
`{1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}`
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∩ B ∩ C)
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read neither Marathi and English newspaper
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read Only one of the newspapers
There are 260 persons with skin disorders. If 150 had been exposed to chemical A, 74 to chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical A but not Chemical B
A college awarded 38 medals in volleyball, 15 in football, and 20 in basketball. The medals awarded to a total of 58 players and only 3 players got medals in all three sports. How many received medals in exactly two of the three sports?
Answer the following:
Write down the following set in set-builder form
{10, 20, 30, 40, 50}
Answer the following:
In a survey of 425 students in a school, it was found that 115 drink apple juice, 160 drink orange juice, and 80 drink both apple as well as orange juice. How many drinks neither apple juice nor orange juice?
Write the following sets in the roaster form.
A = {x | x is a positive integer less than 10 and 2x – 1 is an odd number}
Write the following sets in the roaster form.
C = {x : x2 + 7x – 8 = 0, x ∈ R}
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n + 5 = 8
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n is greater than 4
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in English and Mathematics but not in Science.
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in more than one subject only
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study French and English but not Sanskrit
Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then ______.
