Home
Class 11
MATHS
If A = {x:f(x) =0} and B = {x:g(x) = 0},...

If `A = {x:f(x) =0} and B = {x:g(x) = 0}`, then `A uu B` will be the set of roots of the equation

A

`{f(x)}^(2)+{g(x)}^(2) = 0`

B

`(f(x))/(g(x))`

C

`(g(x))/(f(x))`

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to understand the implications of the sets \( A \) and \( B \) defined by the equations \( f(x) = 0 \) and \( g(x) = 0 \). ### Step-by-Step Solution: 1. **Define the Sets**: - Let \( A = \{ x : f(x) = 0 \} \) be the set of roots of the function \( f(x) \). - Let \( B = \{ x : g(x) = 0 \} \) be the set of roots of the function \( g(x) \). 2. **Union of the Sets**: - The union of sets \( A \) and \( B \), denoted \( A \cup B \), will include all elements that are in either set \( A \) or set \( B \). Therefore, \( A \cup B = \{ x : f(x) = 0 \text{ or } g(x) = 0 \} \). 3. **Roots of the Combined Equation**: - The combined equation that has roots in both sets can be represented as \( f(x) = 0 \) or \( g(x) = 0 \). This means that the roots of the equation formed by taking the union of the roots from both functions will be the values of \( x \) that satisfy either \( f(x) = 0 \) or \( g(x) = 0 \). 4. **Conclusion**: - Thus, \( A \cup B \) will be the set of all roots of the equation formed by the union of the roots of \( f(x) \) and \( g(x) \). ### Final Answer: The set \( A \cup B \) will be the set of roots of the equation \( f(x) = 0 \) or \( g(x) = 0 \). ---
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|22 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

Statement-1 If A = {x |g(x) = 0} and B = {x| f(x) = 0}, then A nn B be a root of {f(x)}^(2) + {g(x)}^(2)=0 Statement-2 x inAnnBimpliesx inAorx inB .

The roots of the equation x^2+ax+b=0 are

Show that A.M. of the roots of x^(2) - 2ax + b^(2) = 0 is equal to the G.M. of the roots of the equation x^(2) - 2b x + a^(2) = 0 and vice- versa.

Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The total number of root(s) of the equation f(x)=g(x) is/ are

Let f(x) = x^(2) - 5x + 6, g(x) = f(|x|), h(x) = |g(x)| The set of values of x such that equation g(x) + |g(x)| = 0 is satisfied contains

if the difference of the roots of the equation x^(2)+ ax +b=0 is equal to the difference of the roots of the equation x^(2) +bx +a =0 ,then

Let f(x) = x^(2) - 5x + 6, g(x) = f(|x|), h(x) = |g(x)| The set of value of mu such that equation h(x) = mu has exactly 8 real and distinct roots, contains. (a) 0 (b) 1/8 (c) 1/16 (d) 1/4

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and betadot

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

Home
Profile