Home
Class 12
MATHS
If alpha, beta, gamma are roots of the e...

If `alpha, beta, gamma` are roots of the equation `x^(3) + px^(2) + qx + r = 0`, then `(alpha + beta) (beta + gamma)(gamma + alpha)` =

Text Solution

Verified by Experts

The correct Answer is:
`-pq +r`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE -2.2 (VERY SHORT ANSWER QUESTIONS)|6 Videos
  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE -2.2 (SHORT ANSWER QUESTIONS)|19 Videos
  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE -2.1 (VERY SHORT ANSWER QUESTIONS)|18 Videos
  • SYSTEM OF CIRCLES

    AAKASH SERIES|Exercise EXERCISE 2.2|22 Videos
  • TRANSFORMATIONS AND INDENTITIES

    AAKASH SERIES|Exercise PRACTIVE EXERCISE|36 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta, gamma are roots of the equation x^(3) + px^(2) + qx + r = 0 , then sum(alpha - beta )^(2) =

If alpha, beta, gamma are roots of the equation x^(3) - px^(2) + qx - r = 0 , then sum alpha^(2) beta =

If alpha, beta, gamma are roots of the equation x^(3) + px^(2) + qx + r = 0 , then sum (1)/(alpha beta ) =

If alpha , beta , gamma are the roots of the equation x^3 - px^2 + qx +r=0 then ( alpha + beta ) ( beta + gamma) ( gamma + alpha)=

If alpha, beta, gamma are roots of the equation x^(3) + px^(2) + qx + r = 0 , then sum alpha^(2) beta^(2) =

If alpha, beta, gamma are roots of the equation px^(3) + qx^(2) + rx + s = 0 then sum alpha^(2) beta^(2) =

If alpha , beta , gamma are the roots of the equation x^3 +px^2 + qx +r=0 prove that ( alpha + beta ) ( beta + gamma) ( gamma + alpha ) =r-pq

If alpha, beta , gamma are the zeros of the polynomial x^(3) - px^(2) + qx - r then 1/(alpha beta) + 1/(beta gamma) + 1/(gamma alpha) = …………..