Home
Class 12
MATHS
If alpha and beta, alpha and gamma, alph...

If `alpha` and `beta`, `alpha` and `gamma`, `alpha` and `delta` are the roots of the equations `ax^(2)+2bx+c=0`, `2bx^(2)+cx+a=0` and `cx^(2)+ax+2b=0` respectively where `a`, `b`, `c` are positive real numbers, then `alpha+alpha^(2)` is equal to

A

`-1`

B

`1`

C

`0`

D

`abc`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `alpha` is root of all equations.
`:.a alpha^(2)+2balpha+c=0`
`2balpha^(2)+calpha+a=0`
`calpha^(2)+aalpha+2b=0`
Adding `(a+2b+c)(1+alpha+alpha^(2))=0`
As `a`,`b`,`c in R^(+)`, `alpha+alpha^(2)=-1`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

If alpha" and "beta, alpha" and "gamma" and "alpha" and "delta are the roots of the equations ax^(2)+2bx+c=0, 2bx^(2)+cx+a=0" and "cx^(2)+ax+2b=0 respectively, where a,b and c are positive real numbers, then alpha+alpha^(2)=

If alpha and beta are thr roots of the equation ax^(2) + bx + c = 0 then ( alpha + beta )^(2) is ……… .

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then (alpha+beta)^(2) is …………..

If the roots of the equation x^(2)+2bx+c=0 are alpha" and "beta, " then "b^(2)-c =

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q(b) (1)/(alpha)+(1)/(beta)

If alpha" and "beta are the solutions of the quadratic equation ax^(2)+bx+c=0 such that beta= alpha^(1/3) , then

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q (a)(alpha)/(beta)+(beta)/(alpha)

Let alpha , beta (a lt b) be the roots of the equation ax^(2)+bx+c=0 . If lim_(xtom) (|ax^(2)+bx+c|)/(ax^(2)+bx+c)=1 then

Let three quadratic equations ax^(2) - 2bx + c = 0, bx^(2) - 2 cx + a = 0 and cx^(2) - ax + b = 0 , all have only positive roots. Then ltbr. Which of these are always ture?