Home
Class 12
MATHS
Concept : Let a(0)x^(n)+a(1)x^(n-1)+…+a(...

Concept : Let `a_(0)x^(n)+a_(1)x^(n-1)+…+a_(n-1)x+a_(n)=0` be the nth degree equation with `a_(0),a_(1),…a_(n)` integers. If p/q is a rational root of this equation, then p is a divisor of `a_(n)` and q is a divisor of `a_(0)`. If `a_(0)=1`, then every rational root of this equation must be an integer.
The rational roots of the equation `3x^(3)-x^(2)-3x+1=0` are in

A

A.P.

B

G.P.

C

H.P.

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise COMPREHENSIONS - III|3 Videos
  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise NUMERICAL BASED|3 Videos
  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise COMPREHENSIONS - I|3 Videos
  • PROGRESSION & SERIES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos
  • SET, RELATION & FUNCTION

    FIITJEE|Exercise Exercise 3|8 Videos

Similar Questions

Explore conceptually related problems

Concept : Let a_(0)x^(n)+a_(1)x^(n-1)+…+a_(n-1)x+a_(n)=0 be the nth degree equation with a_(0),a_(1),…a_(n) integers. If p/q is a rational root of this equation, then p is a divisor of a_(n) and q is a divisor of a_(0) . If a_(0)=1 , then every rational root of this equation must be an integer. The roots of the equation x^(3)-9x^(2)+23x-15=0 , if integers, are in

Let a_(0)x^(n)+a_(1)x^(n-1)+...+a_(n-1)x+a_(n)=0 be the nth degree equation with a_(0),a_(1),...a_(n) integers.If (p)/(q) is arational root of this equation,then p is a divisor of an and q is a divisor of a_(n). If a_(0)=1, then every rationalroot of this equation must be an integer.

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

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

Let f(x)=a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+......+a_(n),(a_(0)!=0) if a_(0)+a_(1)+a+_(2)+......+a_(n)=0 then the root of f(x) is

Let f(x) =a_(0)x^(n)+a_(1)x^(n-1)+...+a_(n)(a_(0)ne0) be a polynomial of degree n . If x+1 is one of its factors, then______.

(1+x)^(n)=a_(0)+a_(1)x+a_(2)x^(2) +......+a_(n)x^(n) then Find the sum of the series a_(0) +a_(2)+a_(4) +……

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) .

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)++a_(2n)x^(2n) find the value of a_(0)+a_(3)+a_(6)++,n in N