Home
Class 12
MATHS
If the roots of the cubic, x^3+a x^2+b x...

If the roots of the cubic, `x^3+a x^2+b x+c=0` are three consecutive positive integers, then the value of `a^2/(b+1)` is equal to __________.

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consecutive positive integers, then the value of (a^2//b+1) is equal to?

If the roots of the cubic x ^(3) +ax ^(2) + bx +c=0 are three consecutive positive integers, then the value of (a ^(2))/(b +1) =

If the roots of the equation x^2-b x+c=0 are two consecutive integers, then find the value of b^2-4c

If the roots of x^(2)-bx+c=0 be two consecutive integers, then find the value of b^(2)-4c .

If the roots of x^2-bx +c=0 are two consecutive integers then b^2-4c=

If a , b , c are consecutive positive integers and (log(1+a c)=2K , then the value of K is (a) logb (b) loga (c) 2 (d) 1

If cos A, cosB and cosC are the roots of the cubic x^3 + ax^2 + bx + c = 0 where A, B, C are the anglesof a triangle then find the value of a^2 – 2b– 2c .

If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c is (a) 0 (b) 1 (c) 2 (d) none of these

If two roots of x^3-a x^2+b x-c=0 are equal in magnitude but opposite in signs, then prove that a b=c

If a,b and c are three consecutive positive integers such that 1/(a!)+1/(b!)=lambda/(c!) then find the value of root under lambda .

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Find the area bounded by the curves y=6x-x^2a n dy=x^2-2xdot

    Text Solution

    |

  2. Consider f(x)=int(-1)^(x)(e^((x-t)/(x-2-t))dt)/(x-2-t)^(2) Q. The gr...

    Text Solution

    |

  3. If the roots of the cubic, x^3+a x^2+b x+c=0 are three consecutive pos...

    Text Solution

    |

  4. sum(n=1)^(prop)tan^(-1)((4n)/(n^(4)+5))=

    Text Solution

    |

  5. lim(n to prop) (n)/(3){((3)/(n)+(9)/(n^(2)))^(2)+((3)/(n)+(18)/(n^(2))...

    Text Solution

    |

  6. Let a differentiable function f:RtoR be such that for all x and y in R...

    Text Solution

    |

  7. The function y=(2x-1)/(x-2),(x!=2) is its own inverse decrease at all...

    Text Solution

    |

  8. The function f(x) = (x^(2) - 1)|x^(2) - 3x + 3|+cos (|x|) is not diffe...

    Text Solution

    |

  9. If vec a= hat i+ hat j+ hat k ,\ vec b=2 hat i- hat j+3 hat k\ a n d...

    Text Solution

    |

  10. Radius of largest circle with center (0, 1) which can be inscribed ...

    Text Solution

    |

  11. Let x1,""x2,"". . . . . . ,""xn be n observations, and let bar x be t...

    Text Solution

    |

  12. If the variable line y=k x+2h is tangent to an ellipse 2x^2+3y^2=6, th...

    Text Solution

    |

  13. The focal chord of the parabola (y-2)^2=16(x-1) is a tangent to the ...

    Text Solution

    |

  14. If vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= h...

    Text Solution

    |

  15. Given three points P, Q, R with P (5, 3) and R lies on the x-axis. I...

    Text Solution

    |

  16. The value of the definite integral int (0)^(pi//2) ((1+ sin 3x)/(1+2 s...

    Text Solution

    |

  17. The minimum area of a triangle formed by any tangent to the elli...

    Text Solution

    |

  18. A number x is chosen at random from the set {1,2,3,4, ………., 100}. Defi...

    Text Solution

    |

  19. If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2...

    Text Solution

    |

  20. Two numbers are selected randomly from the set S={1,2,3,4,5,6} without...

    Text Solution

    |