Home
Class 12
MATHS
If one root of the equation x^(2) + px +...

If one root of the equation `x^(2) + px + q = 0` is square of the other root, then :

A

`p^(3)-(3 p-1) q+q^(2)=0`

B

`p^(3)-(3 p+1) q+q^(2)=0`

C

`p^(3)+(3 p-1) q+q^(2)=0`

D

`p^(3)+(3 p+1) q+q^(2)=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos
  • SETS,RELATIONS AND FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

The sum of the roots of the equation x^(2) + px + q = 0 is equal to the sum of their squares, then :

If one root of the equation ax^(2) + bx + c =0 is reciprocal of the one root of the equation a_(1)x^(2) + b_(1) x + c_(1) = 0 , then :

One root of the equation x^(2) - 5x+ k = 0 is 2. Then k is :

If one root of the equations x^(2) + px +q=0 is 3 times the other , prove that 3p^(2) = 16q.

Roots of the equation x^(2) -2x+ 1 =0 are :

Find the roots of the equation 2x^(2) + 10 x + 20 =0

If one of the roots of the equations x^(2) - 5x=0 is zero then the other roots is :

If the ratio of the roots of the equation a x^(2)+b x+c=0 is equal to the ratio of the roots of the equation x^(2)+x+1=0 , then a, b , c are in

If for all real values of a one root of the equation x^2-3ax + f(a)=0 is double of the other, then f(x) is equal to

If one root of the equation 6x^2 − 2 x + ( λ − 5 ) = 0 be the reciprocal of the other, then λ =

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank
  1. For the equation 3 x^(2)+p x+3=0, p gt 0, if one root is square of the...

    Text Solution

    |

  2. If x^(2)+(a-b) x+(1-a-b)=0, a, b in R has unequal roots for all values...

    Text Solution

    |

  3. If one root of the equation x^(2) + px + q = 0 is square of the other...

    Text Solution

    |

  4. If x^(2)+2 a x+(10-3 a) gt 0 for all x, then

    Text Solution

    |

  5. Let f(x)=a x^(2)+b x+c, a ne 0 and Delta=b^(2)-4 a c . If alpha+beta, ...

    Text Solution

    |

  6. Let a,b,c be the sides of a triangle no two of them are equal and la...

    Text Solution

    |

  7. If alpha, beta are the roots of the equation x^(2)+x+1=0, then the equ...

    Text Solution

    |

  8. Let alpha,beta be the roots of the equation x^(2)-px+r=0 and (alpha)/...

    Text Solution

    |

  9. The smallest value of k for which both the roots of the equation x^(2)...

    Text Solution

    |

  10. The minimum positive value of (x^(2)+2 x+4)/(x+2) is

    Text Solution

    |

  11. Let p and q be real number such that p ne 0 , p^(3) ne q and p^(3...

    Text Solution

    |

  12. If p and q are the roots of the equation x^(2)+p x+q=0 then

    Text Solution

    |

  13. If the difference between the roots of x^(2)+a x+b=0 is same as that o...

    Text Solution

    |

  14. If alpha ne beta and alpha^(2) = 5 alpha - 3, beta^(2) = 5 beta - 3 , ...

    Text Solution

    |

  15. The number of real roots of the equation |x|^(2)-3|x|+2=0 is

    Text Solution

    |

  16. If one root of the equation x^(2)+p x+12=0 is 4, while the equation x^...

    Text Solution

    |

  17. If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a...

    Text Solution

    |

  18. If (1-p) is a root of the quadratic equation x^(2)+p x+(1-p)=0 then it...

    Text Solution

    |

  19. The value of a for which the sum of the squares of the roots of the eq...

    Text Solution

    |

  20. If both the roots of the quadratic equation x^(2)-2 k x+(k^(2)+k-5)=0 ...

    Text Solution

    |