English

Translate the following statements into symbolic form Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0 - Mathematics

Advertisements
Advertisements

Question

Translate the following statements into symbolic form

Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0

Sum

Solution

p: x = 2 is a root of the equation 3x2 – x – 10 = 0.

q: x = 3 is a root of the equation 3x2 – x – 10 = 0.

p ∨ q: Either x = 2 or x = 3 is the root of equation

3x2 – x – 10 = 0.

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Exercise [Page 263]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 14 Mathematical Reasoning
Exercise | Q 5.(vi) | Page 263

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Show that the statement

p: “If x is a real number such that x3 + 4= 0, then x is 0” is true by

(i) direct method

(ii) method of contradiction

(iii) method of contrapositive


Show that the following statement is true by the method of contrapositive.

pIf x is an integer and x2 is even, then x is also even.


Find out the sentence are statement and are not. Justify your answer.

Is the earth round?


Write the negation of the statement:

 The sun is cold.

 

 I will not go to school.


 Both the diagonals of a rectangle have the same length.


For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

A lady gives birth to a baby boy or a baby girl.


Write the component statement of the compound statement and check whether the compound statement is true or false:

 x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.


Check the validity of the statement:

q : 125 is a multiple of 5 and 7.


Check the validity of the statement:

 r : 60 is a multiple of 3 or 5.

 

Determine whether the argument used to check the validity of the following statement is correct:
p : "If x2 is irrational, then x is rational"
The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.


Identify the component statements and the connective in the following compound statements.

2 is a positive number or a negative number.


Write the negation of the following statements:
q: 9 is a multiple of 4.


Rewrite the following statements in the form of conditional statements:

Mohan will be a good student if he studies hard.


Rewrite the following statements in the form of conditional statements:

Ramesh will get dessert only if he eats his dinner.


Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.


Check the validity of the statements:
r: 100 is a multiple of 4 and 5.


Which of the following sentences are statements? Justify

Every square is a rectangle.


Which of the following sentences are statements? Justify

sin2x + cos2x = 0


Find the component statements of the following compound statements.

0 is less than every positive integer and every negative integer.


Find the component statements of the following compound statements.

A rectangle is a quadrilateral or a 5-sided polygon.


Write the component statements of the following compound statements and check whether the compound statement is true or false.

57 is divisible by 2 or 3.


Translate the following statements into symbolic form

2, 3 and 6 are factors of 12


Write down the negation of following compound statements

x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.


Write down the negation of following compound statements

6 is divisible by 2 and 3.


Rewrite the following statements in the form of conditional statements

The unit digit of an integer is 0 or 5 if it is divisible by 5.


Identify the Quantifiers in the following statements.

There exists a even prime number other than 2.


The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.


The negation of the statement “101 is not a multiple of 3” is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×