Home
Class 10
MATHS
If one of the zeros of x^(3) + ax^(2) +...

If one of the zeros of `x^(3) + ax^(2) + bx + c ` is (-1) ,find the product of the other two zeros in terms of a + b

Text Solution

Verified by Experts

The correct Answer is:
`beta gamma = b - a +1`
Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

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

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS ( Higher order thinking skills [HOTS])|10 Videos
  • POLYNOMIALS

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS ( Short answer [SA] type I questions )|27 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

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

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

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

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

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

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 .

The third zero of a polynomial f(x) = 2x^(3) + 3x^(2) - 5x + 10 whose product to two zeros is 5.

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

If one zero of f(x) = 4x^(2) - 8k x - 9 is negative of the other, find k.

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

ZEN PUBLICATION-POLYNOMIALS-ZEN ADDITIONAL QUESTIONS ( Short answer [SA] type II questions )
  1. Find a quadratic polynomial whose sum and product, respectively, of ze...

    Text Solution

    |

  2. If alpha and beta are zeros of f(x) = 6x^(2) + x= 2 find the value fo...

    Text Solution

    |

  3. If alpha and beta are zeros of polynomial f(x) = x^(2) + px + q, form ...

    Text Solution

    |

  4. Find a cubic polynomial with sum, sum of product of its zeros taken t...

    Text Solution

    |

  5. If zeros of a polynomial f(x) = ax^(3) + 3bx^(2) + 3cx + d are in AP...

    Text Solution

    |

  6. If f(x) = x^(3) + x^(2) - ax + b is divisible by x^(2) - x, find value...

    Text Solution

    |

  7. If two of the zeros of a cubic polynomial ax^(3) + bx^(2) + cx + d are...

    Text Solution

    |

  8. If alpha and beta are zeros of the quadratic polynomial x^(2) - (k+6) ...

    Text Solution

    |

  9. If 1 is one of the zeros of the polynomial 7x- x^(3) - 6, find its oth...

    Text Solution

    |

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

    Text Solution

    |

  11. Find the other two zeroes of the polynomial y^(4)+y^(3)-9y^(2)-3y+18 i...

    Text Solution

    |

  12. If one of the zeros of x^(3) + ax^(2) + bx + c is (-1) ,find the pr...

    Text Solution

    |

  13. If a and b are the zeros of the quadratic polynomial f(x) = kx^(2) + 4...

    Text Solution

    |

  14. Obtain the zeros of the quadratic polynomial sqrt(3) x^(2)- 8x + 4 sqr...

    Text Solution

    |

  15. Find a quadratic polynomial whose zeros are 1 and -3 . Verify the rela...

    Text Solution

    |

  16. What real number should to subtracted from the polynomial 3x^(3) + 10x...

    Text Solution

    |

  17. If f(x) = 6x^(4) + 8x^(3) + 17x^(2) + 21x + 7 is divided by g(x) = 3x^...

    Text Solution

    |