Home
Class 12
MATHS
If alphaa n dbeta,alphaa n dgamma,alphaa...

If `alphaa n dbeta,alphaa n dgamma,alphaa n ddelta` are the roots of the equations `a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0,` respectively, where a, b, and c are positive real numbers, then `alpha+alpha^2=` `a b c` b. `a+2b+c` c. `-1` d. `0`

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 PUBLICATION|Exercise Multiple Correct Answer|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION|121 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the equations a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0, respectively, where a, b, and c are positive real numbers, then alpha+alpha^2= a. a b c b. a+2b+c c. -1 d. 0

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal,then a,b,c are in

If a ,b ,c in R^+and 2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.

If x is real and the roots of the equation a x^2+b x+c=0 are imaginary, then prove tat a^2x^2+a b x+a c is always positive.

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in Rdot

If the roots of the equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove that a,b, c are in G.P,

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

Show that the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal if a,b,c are in H.P.

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and betadot

CENGAGE PUBLICATION-THEORY OF EQUATIONS-Single correct Answer
  1. The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab...

    Text Solution

    |

  2. If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, t...

    Text Solution

    |

  3. If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the...

    Text Solution

    |

  4. The product of uncommon real roots of the polynomials p(x)=x^4+2x^3-8...

    Text Solution

    |

  5. Number of values of x satisfying the pair of quadratic equations x^(2)...

    Text Solution

    |

  6. If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a r...

    Text Solution

    |

  7. If the equations x^(2)+2lambdax+lambda^(2)+1=0, lambda in R and ax^(2)...

    Text Solution

    |

  8. If both the roots of lamda(6x^(2)+3)+rx+2x^(2)-1=0 and 6 lamda(2x^(2)+...

    Text Solution

    |

  9. x^(3)+5x^(2)+px+q=0 and x^(3)+7x^(2)+px+r=0 have two roos in common. I...

    Text Solution

    |

  10. Let a,b in N, a != b and the two quadratic equations (a-1)x^2-(a^2+2)x...

    Text Solution

    |

  11. A quadratic equations p(x)=0 having coefficient x^(2) unity is such th...

    Text Solution

    |

  12. If ax^2+bx+c=0 and cx^2+bx+a=0 (a,b,cinR) have a common non-real roots...

    Text Solution

    |

  13. Consdier the equaiton 2 + |x^(2) + 4x + 2= m , m in R Set of all ...

    Text Solution

    |

  14. If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distin...

    Text Solution

    |

  15. Let alpha, beta (a lt b) be the roots of the equation ax^(2)+bx+c=0. I...

    Text Solution

    |

  16. If the quadratic polynomials defined on real coefficient P(x)=a(1)x^...

    Text Solution

    |

  17. For which of the following graphs the quadratic expression y=ax^(2)+bx...

    Text Solution

    |

  18. The difference of maximum and minimum value of (x^(2)+4x+9)/(x^(2)+9) ...

    Text Solution

    |

  19. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  20. All the values of ' a ' for which the quadratic expression a x^2+(a-2)...

    Text Solution

    |