Home
Class 12
MATHS
If a,b,c are real roots of the cubic equ...

If a,b,c are real roots of the cubic equation f(x)=0 such that `(x-1)^(2)` is a factor of f(x)+2 and `(x+1)^(2)` is a factor of f(x)-2, then `abs(ab+bc+ca)` is equal to

Text Solution

Verified by Experts

The correct Answer is:
3
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|6 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Find the number of real roots of the equation f(x) =x^(3) + 2x^(2) +x +2 =0

Number of real roots of equation f(x)=0 is (A) 0 (B) 1 (C) 2 (D) none of these

Let f(x)-2x-x^(2),x<=1 then the roots of the equation f(x)=f^(-1)(x) is

Show that (x-2) is a factor of the polynomial f(x)=2x^(3)-3x^(2)-17x+30 and hence factorize f(x)

Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .

Let f(x) be a polynomial such that f(-(1)/(2))=0, then a factor of f(x) is: 2x-1( b) 2x+1x-1 (d) x+1

if f(x)=3|x|+|x-2| then f'(1) is equal to a)2 b)1 c)3 d)0

If x=2 is a real root of cubic equations f(x)=3x^(3)+bx^(2)+bx+3=0 then the value of lim alue of lim_(x rarr(1)/(2))(e^(f(x))-1)/(2x-1)=

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If a,b,c are real roots of the cubic equation f(x)=0 such that (x-1)^(...

    Text Solution

    |

  2. If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x), then the value...

    Text Solution

    |

  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

    Text Solution

    |

  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

    Text Solution

    |

  5. Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...

    Text Solution

    |

  6. The function f:[0,3] to [1,29], defined by f(x)=2x^(3)-15x^(2)+36x+1 i...

    Text Solution

    |

  7. Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x sat...

    Text Solution

    |

  8. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  9. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  10. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  11. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, wh...

    Text Solution

    |

  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g{f(x)} is invertible in the dom...

    Text Solution

    |

  13. Domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) fo...

    Text Solution

    |

  14. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo)...

    Text Solution

    |

  15. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

  16. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  17. Let E={1,2,3,4}a n dF-{1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  18. Suppose f(x)=(x+1)^2forxgeq-1. If g(x) is the function whose graph is ...

    Text Solution

    |

  19. If f:[1,infty) rarr [2,infty) is given by f(x)=x+1/x, " then " f^(-1)(...

    Text Solution

    |

  20. Let f(x0=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f(x...

    Text Solution

    |

  21. The domain of definition of function of f(x)=(log(2)(x+3))/(x^(2)+3x+2...

    Text Solution

    |