Home
Class 12
MATHS
If the polynomial equation an x^n + a(n-...

If the polynomial equation `a_n x^n + a_(n-1) x^(n-1) + a_(n-2) x^(n-2) + ....... + a_0 = 0, n` being a positive integer, has two different real roots `a` and `b`. then between `a` and `b` the equation `na_n x^(n-1) +(n-1)a_(n-1) x^(n-2) +.......+a_1 =0` has

A

exactly one root

B

atmost one root

C

atleast one root

D

No root

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-I) ( Objective Problems ) (BASED ON LMVT )|2 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-I) ( Objective Problems ) (CURVE SKETCHING, QUESTION ON FINDING NUMBER OF SOLUTIONS )|4 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-I) ( Objective Problems ) ( MAXIMUM & MINIMUM VALUE IN CLOSED INTERVAL BY MONOTONOCITY )|1 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

Similar Questions

Explore conceptually related problems

If the equation a_(n)x^(n)+a_(n-1)x^(n-1)+..+a_(1)x=0, a_(1)!=0, n ge2 , has a positive root x=alpha then the equation na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+….+a_(1)=0 has a positive root which is

Differentiate |x|+a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-1)+...+a_(n-1)x+a_(n)

(1+x)^(n)=a_(0)+a_(1)x+a_(2)*x^(2)+......+a_(n)x^(n) then prove that

Evaluate lim_(xrarrc) f(x) where f(x) = a_nx^n+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+.....+a_2x^2+a_1x^1+a_0

Let a_(0)/(n+1) +a_(1)/n + a_(2)/(n-1) + ….. +(a_(n)-1)/2 +a_(n)=0 . Show that there exists at least one real x between 0 and 1 such that a_(0)x^(n) + a_(1)x^(n-1) + …..+ a_(n)=0

Prove that if the equation a_(0)x^(n)+a_(1)x^(n-1)+….+ a_(n-1) x = 0 has a positive root x_(0) , then the equation na_(0)x^(n-1) +(n-1) a_(1)x^(n-2) +….+ a_(n-1) =0 has a positive root less than x_(0) .

Let f(x) = a_(0)x^(n) + a_(1)x^(n-1) + a_(2) x^(n-2) + …. + a_(n-1)x + a_(n) , where a_(0), a_(1), a_(2),...., a_(n) are real numbers. If f(x) is divided by (ax - b), then the remainder is

If the sequence {a_n}, satisfies the recurrence, a_(n+1) = 3a_n - 2a_(n-1), n ge2, a_0 = 2, a_1 = 3, then a_2007 is

If the equation a_0x^n +a_1x^(n-1) +....a_(n-1)x=0 has a positive root alpha prove that the equation na_0x^(n-1) +(n-1)a_1 x^(n-2) + ---+a_(n-1) = 0 also has a positive root smaller than alpha

Differentiate the following with respect of x:a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)++a_(n-1)x+a_(n)