Home
Class 12
MATHS
Let P (x) be a cubic polynomical with le...

Let P (x) be a cubic polynomical with leading co-efficient unity. Let the remainder when P (x) is divided by `x ^(2)-5x+6` equals 2 times the remainder when P (x) is divided by `x ^(2)-5x+4.` If `P (0)=100,` find the sum of the digits of `P (5),`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise MATCHING TYPE PROBLEMS|6 Videos

  • ELLIPSE

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|2 Videos

  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

Find the remainder when x^3+4x^2-7x+6 is divided by x-1.

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

Find the remainder when x^4+x^3-2x^2+x+1 is divided by x-1 .

Let p(x)=x^4-3x^2+2x+5. Find the remainder when p(x) is divided by (x-1)dot

Find the quotient and remainder when x^4 +8x^3 +x-5 is divided by x+2.

If the remainders of the polynomial f(x) when divided by x-1, x-2 are 2, 5 then the remainder of f(x) when divided by (x-1)(x-2) is

Find the remainder when p(x)=x^3-a x^2+6x-a is divided by (x-a)dot

Find the remainder when p(x)=x^3-a x^2+6x-a is divided by (x-a)dot

Find the remainder when f(x)=9x^3-3x^2+x-5, is divided by g(x)=x-2/3

VIKAS GUPTA (BLACK BOOK) ENGLISH-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x...

    Text Solution

    |

  2. Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=...

    Text Solution

    |

  3. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

    Text Solution

    |

  4. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  5. Let f(x)= cx+d/ax+b ​ . Then fof(x) = x provided that.

    Text Solution

    |

  6. Let A = {x|x ^(2) -4x+ 3 lt 0 , x in R} B={x|2^(1-x)+p le 0;x^2-2(p+7...

    Text Solution

    |

  7. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  8. If f(x) is an even function then find the number of distinct real numb...

    Text Solution

    |

  9. The least integral value of m, m inR for which the range of function ...

    Text Solution

    |

  10. Let x1, x2, x3 satisfying the equation x^3 - x^2 + betax + gamma = 0 ...

    Text Solution

    |

  11. Let A={1,2,3,4}and B={0,1,2,3,4,5}. If 'm' is the number of strictly i...

    Text Solution

    |

  12. The value of sum(r=1)^1024 [log2 r] is equal to, ([.] denotes the gre...

    Text Solution

    |

  13. Let f (x) = (ax+b)/(xc+d), where a,b,c d are non zero If f (7) =7,f (1...

    Text Solution

    |

  14. It is pouring down rain and the amount of rain hitting point (x,y) is ...

    Text Solution

    |

  15. Let P (x) be a cubic polynomical with leading co-efficient unity. Let ...

    Text Solution

    |

  16. Let f (x) = x^(2)+10x+20. Find the number of real solution of the equa...

    Text Solution

    |

  17. If range of f (x)= ((ln x) (ln x ^(2))+ln x ^(3)+3)/(ln ^(2) x+ln x ^(...

    Text Solution

    |

  18. Polynomial P(x) contains only terms of aodd degree. when P(x) is divid...

    Text Solution

    |

  19. The equation 2x ^(3) -3x ^(2) +p=0 has three real roots. Then find the...

    Text Solution

    |

  20. Find the number of integers in the domain of f (x) = (1)/(sqrt(ln cos ...

    Text Solution

    |