Home
Class 12
MATHS
Let f(x)=-ax^2-b|x|-c, -alpha le x lt 0,...

Let `f(x)=-ax^2-b|x|-c, -alpha le x lt 0, ax^2+b|x|+c 0 le x le alpha` where a,b,c are positive and `alpha gt 0`, then- Statement-1 : The equation f(x)=0has atleast one real root for `x in [-alpha,alpha]` Statement-2: Values of `f(-alpha) and f(alpha)` are opposite in sign.

A

Statement I is correct, Statement II is also correct, Statement II is the correct explanation of Statement I

B

Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I

C

Statement I is correct, Statement II is incorrect

D

Statement I is incorrect, Statement II is correct.

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|1 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If x and alpha are real, then the inequation log_(2)x+log_(x)2+2cos alpha le 0

Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha beta < 0 and f(alpha) f(beta) < 0 f . Then the equation f(x)=0 has three equal real roots one negative root if f(alpha) (a) 0 and f(beta) (b) one positive root if f(alpha) (c) 0 and f(beta) (d) none of these

Let f(x)=x^3+2x^2+x+5. Show that f(x)=0 has only one real root alpha such that [alpha]=-3

If for some differentiable function f(alpha)=0 and f'(alpha)=0, Statement 1: Then sign of f(x) does not change in the neighbourhood of x=alpha Statement 2:alpha is repeated root of f(x)=0

If root of the equation x^(2) + ax + b = 0 are alpha , beta , then the roots of x^(2) + (2 alpha + a) x + alpha^(2) + a alpha + b = 0 are