Home
Class 12
MATHS
Consider the following figure. Answ...

Consider the following figure.

Answer the following questions
(i) What are the roots of the f(x) = 0?
(ii) What are the roots of the f(x) = 4?
(iii)What are the roots of the f(x) = g (x)?

Text Solution

Verified by Experts

(i) For the roots of the equation f(x) = 0, we check the points of intersection of y = f(x) with x -axis at x = - 1 and x = 2, which are roots of the equation f(x) = 0 .
(ii) For the roors of the equation f(x) = 4, we check the points of intersection of the graphs y = f(x) and y = 4 ( a line parallel to x-axis at height 4 units above it)
The x -values of the poinst of intersection of graphs is x = -2 and x = 3 , which are roots of the equation f(x) = 4.
(iii) For the roots of the equation f(x) = g(x), we check the points of intersection of the graphs y = f(x) and y = g(x).
The x -velues of the points of intersection of graphs are x = -2 and x = 4, which are roots of the equation f(x) = g(x)
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.2|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

Consider the graph of y = f(x) as shown in the following figure. (i) Find the sum of the roots of the equation f (x) = 0. (ii) Find the product of the roots of the equation f(x) = 4. (iii) Find the absolute value of the difference of the roots of the equation f(x) = x+2 .

If f(x) = 0 has n roots, then f'(x) = 0 has ………..roots

Graph of y = f(x) is as shown in the following figure. Find the roots of the following equations f(x) = 0 f(x) = 4 f(x) = x + 2

Following is the graph of y = f' (x) , given that f(c) = 0. Analyse the graph and answer the following questions. (a) How many times the graph of y = f(x) will intersect the x - axis? (b) Discuss the type of roots of the equation f (x) = 0, a le x le b . (c) How many points of inflection the graph of y = f(x), a le x le b , has? (d) Find the points of local maxima/minima of y = f(x), a lt x b . (e) How many roots equation f''(x) = 0 has?

Let f(x) be a quadratic polynomial satisfying f(2) + f(4) = 0. If unity is one root of f(x) = 0 then find the other root.

Let f(x)=x^(3)+x+1 , let p(x) be a cubic polynomial such that the roots of p(x)=0 are the squares of the roots of f(x)=0 , then

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

A function f(x) is such that f(x)=0 has 8 distinct real roots and f(4+x)=f(4-x) for x in R . Sum of real roots of the equation f(x)=0 is

The graph of y = f(x) is as shown in the following figure. Find the following values (i) f(-3)" "(ii) f(-2)" "(iii) f(0) (iv) f(2)" "(v) f(3)" "(vi) lim_(x to -3) f(x) (vii) lim_(x to 0) f(x)" "(viii)lim_(x to 2) f(x)" "(ix) lim_(x to 3) f(x) (x) lim_(x to 2^(-)) f(x)" "(xi)lim_(x to -2^(+)) f (x)" "(x ii)lim_(x to 0^(-)) f(x) (x iii) lim_(x to 0^(+)) f(x)