Home
Class 9
MATHS
Find the quadratic equation whose roots ...

Find the quadratic equation whose roots are 2 times the roots of `x^(2) - 12x - 13 = 0`.

A

`x^(2) - 24x - 52 = 0`

B

`x^(2) - 24x - 26 = 0`

C

`x^(2) - 14x - 15 = 0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x) = x^(2) - 12x - 13 = 0`
If the roots of `g(x)` are 2 times the roots of `f(x)` , then
`g(x) = f(x/2) - 13 = 0`
`rArr (x/2)^(2) - 12(x/2) - 13 = 0`
`rArr (x^(2))/(4) - (12x)/(2) - 13 = 0`
`rArr x^(2) - 24 x - 52 = 0`.
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    PEARSON IIT JEE FOUNDATION|Exercise Level 2|19 Videos

  • PROBABILITY

    PEARSON IIT JEE FOUNDATION|Exercise LEVEL 3|8 Videos

  • RATIO, PROPORTION AND VARIATION

    PEARSON IIT JEE FOUNDATION|Exercise Leval 3|10 Videos

Similar Questions

Explore conceptually related problems

Find the equation whose roots are 2 times the roots of x^(5)+2x^(2)-4x+1=0

The quadratic equation whose roots are twice the roots of x^2-3x+3=0 is _____ .

The equation whose roots are 2 times the roots of x^(3)+3x^(2)-5x+1=0 is

For a quadratic equation whose roots are 4 and -12.

The quadratic equation whose roots are square of equation x^(2)-4x+3=0

Find the quadratic equation whose roots are reciprocals of the roots of the equation 7x^(2) - 2x +9 = 0 .

Find the equation whose roots are n xx the roots of the equation ax^(2)+bx+c=0

Find the quadratic equation in x whose roots are (-7)/(2) and (8)/(3) .

PEARSON IIT JEE FOUNDATION-QUADRATIC EXPRESSIONS AND EQUATIONS-Level 3
  1. The equation sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) has

    Text Solution

    |

  2. Out of the group of employees, twice the square root of the number of ...

    Text Solution

    |

  3. Find the quadratic equation whose roots are 2 times the roots of x^(2)...

    Text Solution

    |

  4. If one of the roots of ax^(2) + bx + c = 0 is thrice that of the other...

    Text Solution

    |

  5. If alpha, beta are the roots of px^(2) + qx + r = 0, then alpha^(3) + ...

    Text Solution

    |

  6. If alpha and betaare the roots of x^(2) - (a+1)x + 1/2 (a^(2) + a+1) ...

    Text Solution

    |

  7. The number of roots of the equation 2|x|^(2) - 7|x| + 6 = 0

    Text Solution

    |

  8. In a quadratic equation ax^(2)- bx + c = 0, a,b,c are distinct primes...

    Text Solution

    |

  9. Maximum value of (2+12x-3x^(2))/(2x^(2) - 8x + 9) is "".

    Text Solution

    |

  10. If x^(2) + ax+ b and x^(2) + bx + c have a common factor (x-k), then k...

    Text Solution

    |

  11. If 9x-3y + z = 0 , then the value of y/(2x)+ sqrt((x^(2) - 4xz)/(4x^...

    Text Solution

    |

  12. If the roots of 3x^(2)- 12x +k = 0 are complex, then find the range of...

    Text Solution

    |

  13. If alpha, beta are the roots of ax^(2) + bx + c = 0, then find the qua...

    Text Solution

    |

  14. Ramu swims a distance of 3 km each upstream and downstream. The total ...

    Text Solution

    |

  15. In solving a quadratic equation x^(2) + px + q = 0 a student made a mi...

    Text Solution

    |

  16. The roots of ax^(2) - bx + 2x = 0 are in the ratio of 2 : 3, then "".

    Text Solution

    |

  17. If the roots of 9x^(2) - 2x +7 = 0 are 2 more than the roots of ax^(2)...

    Text Solution

    |

  18. If roots of ax^(2) + bx + c = 0are 2 , more than the roots of px^(2) ...

    Text Solution

    |

  19. If the roots of 2x^(2) + 7x + 5 = 0 are the reciprocal roots of ax^(2)...

    Text Solution

    |

  20. If the roots of the equation ax^(2) + bx + c= 0 is 1/k times the roots...

    Text Solution

    |