Home
Class 10
MATHS
If the quadratic equation p x^2 - 2 sqr...

If the quadratic equation ` p x^2 - 2 sqrt(5)px + 15 = 0` has two equal roots, then find value of p.

Text Solution

Verified by Experts

The correct Answer is:
p=3
The given equation is of the form `ax^(2)+bx+c=0,` where
`a=pmb=-2sqrt(5)p" and "c=15.`
`:." "D=(b^(2)-4ac)=(20p^(2)-60p).`
So, `D=0implies20p^(2)-60p=0implies20p(p-3)=0impliesp=3." "[becausepne0]`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    RS AGGARWAL|Exercise Exercise 4E|71 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

If the quadratic equation px^(2)-2sqrt(5)px+15=0 has two equal roots,then find the value of p

If the quadratic equation px^(2)-2sqrt(5)+15=0 has two equal roots then find value of p.

If the quadratic equation 4 x^ 2 - (p-2)x+ 1 = 0 has equal roots, then the value of 'p' are

The quadratic equation 2x^2 + px + 3 = 0 has two equal roots. Find the value of p.

The quadratic equation 2x^(2) + px + 3 = 0 has two equal roots if p = ______

The quadratic equation 2x^(2) + px + 3 = 0 has two equal roots if p = …………. .

Find the value(s) of k for which the quadratic equation x^(2) + 2sqrt(2)kx + 18 = 0 has equal roots.

If the roots of the quadratic equation 4x^(2) -16x + p = 0 , are real and unequal, then find the value/s of p.

If -4 is the root of the equation x^(2)+kx-4=0 and the quadratic equation x^(2)+px+k=0 has equal roots then find values of k and p

If -5 is a root of the quadratic equation 2x^(2)+px-15=0 and the quadratic equation p(x^(2)+x)+k=0 has equal roots, find the value of k.

RS AGGARWAL-QUADRATIC EQUATIONS -Test Yourself
  1. The roots of the quadratic equation 2x^2 - x - 6 = 0 are

    Text Solution

    |

  2. Find the discriminant of the quadratic equation 3sqrt3x^2+10x+sqrt3=0.

    Text Solution

    |

  3. If the roots of the quadratic equation 2x^(2)+8x+k=0 are equal, find t...

    Text Solution

    |

  4. If the quadratic equation p x^2 - 2 sqrt(5)px + 15 = 0 has two equal ...

    Text Solution

    |

  5. If 1 is a root of the equation ay^(2)+ay+3=0" and "y^(2)+y+b=0 then fi...

    Text Solution

    |

  6. If one zero of the polynomial x^3-4x+1 is 2+sqrt3 write the other zero

    Text Solution

    |

  7. If one root of the quadratic equation 3x^(2)-10x+k=0 is reciprocal of ...

    Text Solution

    |

  8. Find the value of p for which the roots of the equation px (x — 2) + 6...

    Text Solution

    |

  9. Find the value(s) of k so that, the quadratic equation x^2 - 4kx + k =...

    Text Solution

    |

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

    Text Solution

    |

  11. Solve: x^2-(sqrt3+1)x+sqrt3 = 0

    Text Solution

    |

  12. Solve: 2x^2+a x-a^2=0

    Text Solution

    |

  13. Find the roots of the following quadratic equations by the factorisati...

    Text Solution

    |

  14. Solve : sqrt(3)x^(2)+10x-8sqrt(3)=0.

    Text Solution

    |

  15. Solve for x sqrt3x^2-2sqrt(2)x-2sqrt3=0

    Text Solution

    |

  16. Solve by factorization: 4sqrt(3)x^2+5x-2sqrt(3)=0

    Text Solution

    |

  17. Solve by factorization: 4x^2+4b x-(a^2-b^2)=0

    Text Solution

    |

  18. Solve x^(2)+5x-(a^(2)+a-6)=0.

    Text Solution

    |

  19. Solve for x: x^2+6x-(a^2+2a-8)=0

    Text Solution

    |

  20. Find the roots of each of the following equations, if they exist, by a...

    Text Solution

    |