Home
Class 10
MATHS
For what values of k are the roots of th...

For what values of k are the roots of the quadratic equation `3x^(2)+2kx+27=0` real and equal?

Text Solution

Verified by Experts

The correct Answer is:
`k=9" or "k=-9`
`D=4k^(2)-324`. For real and equal roots, we must have, D=0.
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    RS AGGARWAL|Exercise Exercise 4E|71 Videos

  • QUADRATIC EQUATIONS

    RS AGGARWAL|Exercise Test Yourself|55 Videos

  • QUADRATIC EQUATIONS

    RS AGGARWAL|Exercise Exercise 4C|36 Videos

  • PROBABILITY

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|37 Videos

  • REAL NUMBERS

    RS AGGARWAL|Exercise Test Youself|20 Videos

Similar Questions

Explore conceptually related problems

For what value of k are the roots of the quadratic equation kx(x-2sqrt(5))+10=0 real and equal?

For what value of k, are the roots of the quadratic equation kx(x-2)+6=0 equal ?

If the roots of the quadratic equation x^(2) +2x+k =0 are real, then

Find the nonzero value of k for which the roots of the quadratic equation 9x^(2)-3kx+k=0 are real and equal.

Solve the following question. (i) Find the value of k for which the roots of quadratic equation kx^2+2x+3=0 are real and equal.

Find the value of k for which the roots of the quadratic equation 2x^(2) + kx + 8 = 0 will have equal value.

Find k, if the roots of the quadratic equation kx^2-4x+4=0 are equal

Find k, if the roots of the quadratic equation kx^2-4x+4=0 are equal

Find the value of k for which the roots of the quadratic equation 2x^(2)+kx+8=0 will have the equal roots ?

RS AGGARWAL-QUADRATIC EQUATIONS -Exercise 4D
  1. Show that the equation 2(a^2+b^2)x^2+2(a+b)x+1=0 has no real roots whe...

    Text Solution

    |

  2. Show that the roots of the equation x^2 + px - q^2 = 0 are real for al...

    Text Solution

    |

  3. For what values of k are the roots of the quadratic equation 3x^(2)+2k...

    Text Solution

    |

  4. For what value of k are the roots of the quadratic equation kx(x-2sqrt...

    Text Solution

    |

  5. Find the value of p for which the quadratic equation 4x^2+px+3=0 has e...

    Text Solution

    |

  6. Find the nonzero value of k for which the roots of the quadratic equat...

    Text Solution

    |

  7. (i) Find the values of k for which the quadratic equation (3k+1)x^(2)+...

    Text Solution

    |

  8. Find the values of p for whch the equadratic equation (2p+1)x^2-(7p+2)...

    Text Solution

    |

  9. Find the value of p for which the quadratic equation (p+1)x^2+ -6(p+1)...

    Text Solution

    |

  10. If -5 is a root of the quadratic equation 2x^2+p x-15=0 and the quadra...

    Text Solution

    |

  11. If 3 is a root of the quadratic equation x^(2)-x+k=0 find the value of...

    Text Solution

    |

  12. If -4 is a root of the equation x^2+2x+4p=0 then find the value of k f...

    Text Solution

    |

  13. If the equation (1+m^2)x^2+2m c x+(c^2-a^2)=0 has equal roots, prove t...

    Text Solution

    |

  14. If the roots of the equation (c^2-a b)x^2-2(a^2-b c)x+b^2-a c=0 are eq...

    Text Solution

    |

  15. Find the values of p fro which the qadratic equation 2x^(2)+px+8=0 has...

    Text Solution

    |

  16. Find the value of alpha for which the equation (alpha-12)x^(2)+2(alpha...

    Text Solution

    |

  17. For what real values of k the equation 9x^2 +8 Kx +16=0 have real and ...

    Text Solution

    |

  18. Find the values of k for which the given quadratic equation has real a...

    Text Solution

    |

  19. If a and b are real and aneb then show that the roots of the equation ...

    Text Solution

    |

  20. If the roots of the equation (a^2+b^2)x^2-2(a c+b d)x+(c^2+d^2)=0 are ...

    Text Solution

    |