Home
Class 12
MATHS
The equation f (x) = 0 possesses same si...

The equation `f (x) = 0` possesses same signs for `f (a)` and `f (b)`, then

A

at least one root of the equation lies in `a lt x lt b`

B

either no root or an even number of roots lie in the interval `a lt x lt b`

C

any number of roots may lie in `a lt x lt b`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • NUMERICAL METHODS

    ML KHANNA|Exercise SELF ASSESSMENT TEST|10 Videos

  • MEASURES OF CENTRAL TENDENCY

    ML KHANNA|Exercise ASSERTION / REASON|1 Videos

  • PAIR OF STRAIGHT LINES

    ML KHANNA|Exercise SELF ASSESSMENT TEST|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^2-ax + b, where a is an odd positive integer and the roots of the equation f(x) = 0 are two distinct prime numbers. If a + b = 35 then, the value of ([f(0)+f(2)+f(3)+...+f(10)] xx f(10))/440=0........

If f(x)=ax+b and the equation f(x)=f^(-1)(x) be satisfied by every real value of x, then

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y) for all x y in R, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2 , then prove that f' = 2f(x) .

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b, "then " int_(0)^(a) f(x) dx +int_(0)^(b) f^(-1) (x) dx is equal to

Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x) .A quadratic expression f(x) has same sign as that coefficient of x^2 for all real x if and only if the roots of the corresponding equation f(x)=0 are imaginary.If F(x)=int_a^(x^3) g(t)dt, the F(x) is (A) an incresing function in R (B) an increasing function only in [0,oo) (C) a decreasing function R (D) a decreasing function only in [0,oo)