Home
Class 10
MATHS
If two zeros of f(x) = x^(3) - 4x^(2) - ...

If two zeros of `f(x) = x^(3) - 4x^(2) - 3x + 12 are sqrt(3) and - sqrt(3)`, find its third zero.

Text Solution

Verified by Experts

The correct Answer is:
`gamma = 4`
Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS ( Short answer [SA] type II questions )|17 Videos
  • POLYNOMIALS

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS ( Long answer [LA] type questions )|13 Videos
  • POLYNOMIALS

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS (Very short answer [VSA] type questions (Answer the following questions :))|10 Videos
  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    ZEN PUBLICATION|Exercise ADDITIONAL QUESTIONS - HIGHER ORDER THINKING SKILLS (HOTS)|12 Videos
  • PROBABILITY

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS HOTS [HIGHER ORDER THINKING SKILLS]-QUESTIONS|24 Videos

Similar Questions

Explore conceptually related problems

If two zeros of a polynomial p(x) = x^(3) - 4x^(2) - 3x + 12 " are " sqrt(3) and - sqrt(3) , find its 3 rd zero .

If zeros of f(x) = x^(3) - 12 x^(2) + 39 x + k are in AP, find k.

If zeros of f(x) = x^(3) - 12 ^(2) + 39 x + k are in A.P., find k.

Find the condition which must be satisfied by the zeros of f(x) = x^(3) - px^(2) + qx - r , when the sum of its two zeros is zero .

Find the other zeros of 2x^(4) - 10x^(3) + 5x^(2) + 15x - 12 given that sqrt((3)/(2)) and - sqrt((3)/(2)) are two of its zeros .

Find the zeros of f(x) = x^(3) - 5x^(2) - 2 x + 24 , if the product of its two zeros is 12 .

If zeros of x^(3) - 3x^(2) + x+ 1 are a-b, a,a+b, find a and b.

sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

The function f(x)=2x^(3)-3x^(2)-12x+4 has :

ZEN PUBLICATION-POLYNOMIALS-ZEN ADDITIONAL QUESTIONS ( Short answer [SA] type I questions )
  1. If alpha and beta are zeros of p(x) = 4x^(2) + 3x + 7 , "find" (1)/(a...

    Text Solution

    |

  2. If one zero of f(x) = (k^(2) +4) x^(2) + 13x + 4k is the reciprocal of...

    Text Solution

    |

  3. If alpha , beta, and gamma are the zeroa od f(x) = ax^(3) + bx^(2) +c...

    Text Solution

    |

  4. If alpha, beta, and gamma are the zeros of 2x^(3) - 4x^(2) + 6x +9, fi...

    Text Solution

    |

  5. If zeros of a quadratic polynomial x^(2) + (a +1) x + b are 2 and -3, ...

    Text Solution

    |

  6. Find zeros of polynomials by the algebraic method and verify the relat...

    Text Solution

    |

  7. Given f(x+1) = 3x +5 , evaluate f(-2) and f(x)

    Text Solution

    |

  8. If the product of the zeros of a polynomial (ax^(2) - 6x - 6) is 4, fi...

    Text Solution

    |

  9. If alpha and beta are the zeros of the quadratic polynomial 4x^(2) + 4...

    Text Solution

    |

  10. Find values of p for which the quadratic polynomial 4x^(2) + px +3 h...

    Text Solution

    |

  11. Find a if one zero of (a^(2) +9) x^(2) + 13x + 6a is a reciprocal of...

    Text Solution

    |

  12. If two zeros of f(x) = x^(3) - 4x^(2) - 3x + 12 are sqrt(3) and - sqrt...

    Text Solution

    |

  13. Without solving, find the value of m for which the zeros are equal fo...

    Text Solution

    |

  14. Find values of k for which (k +4) x^(2) + (k +1) x+1 has equal zeros.

    Text Solution

    |

  15. The sum and product of the zeroes an a quadratic polynomial P (x) = ax...

    Text Solution

    |

  16. Find the quotient and the remainder when P (x) = 3x^(3)+ x^(2)+2x+5 is...

    Text Solution

    |

  17. Sum and product of the zeroes of a quadratic polynomial P(x) = ax^(2)...

    Text Solution

    |

  18. Find the value of k of polynomial P(x) = x^(2) - x - (2k +2) in whic...

    Text Solution

    |

  19. If one zero of the polynomial p(x) = x^(2) - 6x + k is twice the other...

    Text Solution

    |

  20. Find the polynomial of least degree that should be subtracted from p(x...

    Text Solution

    |