Home
Class 11
MATHS
Prove that ap+q=0 if f(x)=x^3-3px+2q is ...

Prove that `ap+q=0 if f(x)=x^3-3px+2q` is divisible by`g(x)=x^(2)+2ax+a^(2).`

Promotional Banner

Topper's Solved these Questions

  • BASIC ALGEBRA

    FULL MARKS|Exercise Additional Question sloved|32 Videos

  • BASIC ALGEBRA

    FULL MARKS|Exercise Exercise-2.1|5 Videos

  • BINOMIAL THEOREM, SEQUENCES AND SERIES

    FULL MARKS|Exercise Additional Questions Solved|31 Videos

Similar Questions

Explore conceptually related problems

Prove that p + q = 0 " if " x^(3) - 3px + 2q " is divisible by" (x + 1)^(2)

If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of f(2)dot

Find the remainder when f (x) =x ^(4) - 3x ^(2) + 4 is divided by g (x) =x -2 and verify the result by actual division .

If f (x) = 2x-3 and g(x)= x^(2) +x-2 then go f(x) is

If f(x)=x^3+x^2-a x+b is divisible by x^2-x , then find the value of a and b

Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is divisible by x^2 + 1 , then

The sum of the polynomials p(x) =x^(3) -x^(2) -2, q(x) =x^(2) -3x+ 1

If p(x)=x^2-3x+2x^3+5 and q(x)=x^2+2x+4, the find p(x)+q(x).

If f(x)=2x-3 and g(x)=x^2+x-2 , then gof(x) is

The sum of the polynomials p(x) = x^(3) - x^(2) - 2, q(x) = x^(2) - 3x + 1

FULL MARKS-BASIC ALGEBRA-Exercise-2.13
  1. Prove that ap+q=0 if f(x)=x^3-3px+2q is divisible byg(x)=x^(2)+2ax+a^(...

    Text Solution

    |

  2. If |x + 2| le 9 , then x belongs to

    Text Solution

    |

  3. Given that x, y and b are real numbers x lt y, b gt 0, then

    Text Solution

    |

  4. If (|x-2|)/(x - 2) ge 0, then x belongs to

    Text Solution

    |

  5. The solution of 5x-1lt24 and 5x+1gt-24 is ……..

    Text Solution

    |

  6. The solution set of the following inequality |x - 1| le |x - 3| is

    Text Solution

    |

  7. The value of log(sqrt2)512 is …..

    Text Solution

    |

  8. The value of log(3)""1/81 is …….

    Text Solution

    |

  9. If log(sqrtx)0.25=4 then the value of x is ………

    Text Solution

    |

  10. The value of "log"(a) b "log"(b)c "log"(c ) a is

    Text Solution

    |

  11. If 3 is the logarthim of 343, then the base is ……

    Text Solution

    |

  12. Find a so that the sum and product of the roots of the equation 2x^(2)...

    Text Solution

    |

  13. If a and b are roots of the equation x^(2)-kx+16=0 and satisfy a^(2)+b...

    Text Solution

    |

  14. The number of solutions of x^(2) + |x - 1| = 1 is

    Text Solution

    |

  15. The equation whose roots are numerically equal but opposite in sign to...

    Text Solution

    |

  16. If 8 and 2 are the roots of x^(2) + ax + c = 0 and 3,3 are the roots o...

    Text Solution

    |

  17. If a and b are the real roots of the equation x^(2)-kx+c=0 , then the ...

    Text Solution

    |

  18. If (kx)/((x + 2) (x - 1)) = (2)/(x + 2) + (1)/(x -1) , then the value ...

    Text Solution

    |

  19. If (kx)/((x+2)(x-1))=(2(x-1)+1(x+2))/((x+2)(x-1)) =(3x)/(x+2)(x-1) i...

    Text Solution

    |

  20. The number of roots of (x + 3)^(4) + (x + 5)^(4) = 16 is

    Text Solution

    |

  21. The value of "log"(3)11."log"(11) 13."log"(13)15."log"(15)27."log"(27)...

    Text Solution

    |