Question

MCQ (100)
Q55. If f(x) is continuous in (a, b) and if f(a) and
f(b) are of opposite signs then the equation
f(x) = 0 will have at least between 'a' and
'b'.
(A) Two real roots
(B) Three real roots
(C) One real root
(D) No root​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If f(x) is continuous in (a, b) and if f(a) and f(b) are of opposite signs then the equation f(x) = 0 will have at least _____ between 'a' and 'b'.

(A) Two real roots

(B) Three real roots

(C) One real root

(D) No root

EVALUATION

The polynomial f(x) is continuous function of x

So while x changes from a to b , f(x) must goes through all the values from f(a) to f(b).

But f(a) and f(b) are of opposite signs , so one of the quantities f(a) or f(b) is positive and other is negative , it follows that at least one value of x say c lying between a and b , f(x) must be zero

So c is the required root

Hence If f(x) is continuous in (a, b) and if f(a) and f(b) are of opposite signs then the equation f(x) = 0 will have at least one real root between 'a' and 'b'.

FINAL ANSWER

Hence the correct option is

(C) One real root

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ consider the above set A. Insert the appropriate symbol E of E/ in each of the following blank spaces (a) -3...A (b) 9...

https://brainly.in/question/28046206

2. if A ={2,3} and B= { x|x is solution of x^2 + 5x + 6= 0}

Are there A and B equal set or disjoint set?

https://brainly.in/question/21681247