Home
Class 12
MATHS
If x1,x2,x3,x4 be the roots of the equat...

If `x_1,x_2,x_3,x_4` be the roots of the equation`x^4 + a x^3+b x^2 +cx + d =0`. If `x_1 +x_2 = x_3 + x_4` and `a,b,c,d in R`,then (i) lf a =2, then the value of b-c (ii) `b <0`, then how many different values of a, we may have

A

`(-oo,(1)/(4))`

B

`(-oo,3)`

C

`(-oo,1)`

D

`(-oo,4)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise EXAMPLE|6 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

If x_(1),x_(2),x_(3),x_(4) be the roots of the equation x^(4)+ax^(3)+bx^(2)+cx+d=0. If x_(1)+x_(2)=x_(3)+x_(4) and a,b,c,d in R, then ( i ) If a =2, then the value of b-c( ii) b<0, then how many different values of a,we may have

If 1,2,3 and 4 are the roots of the equation x^(4)+ax^(3)+bx^(2)+cx+d=0, then a+2b+c=

If a,b are the roots of the equation x^(2)+x+1=0, thn a^(2)+b^(2)= a.1b.2c-1d.3

Let x_1,x_2 be the roots of the equation x^2-3x+A=0 and x_3,x_4 be those of equation x^2-12x+B=0 and x_1,x_2,x_3,x_4 form an increasing G.P. find A and B.

If a and b are roots of the equation x^2+a x+b=0 , then a+b= (a) 1 (b) 2 (c) -2 (d) -1

Number of roots of equation 3^(|x|)-|2-|x||=1 is a.0 b.2 c.4d.7

If 4:3=x^(2):12, then the value of x(x>0)16( b) 4(c)9(d)3

The number of real roots of equation x^8-x^5+x^2-x+1=0 is (A) 2 (B) 4 (C) 6 (D) 0

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If x1,x2,x3,x4 be the roots of the equationx^4 + a x^3+b x^2 +cx + d =...

    Text Solution

    |

  2. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

    Text Solution

    |

  3. The number of points in (-oo,oo) for which x^(2)-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|} has a local minimum or a loca...

    Text Solution

    |

  7. A rectagular sheet of fixed permeter with sides having thir lengths in...

    Text Solution

    |

  8. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  10. e total number of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  13. If f(x)=x^(3)+bx^(2)+cx+dand 0 ltb^(2)ltc, then in (-oo,oo)

    Text Solution

    |

  14. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

    Text Solution

    |

  15. The length of a longest interval in which the function 3sinx-4sin^(3...

    Text Solution

    |

  16. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  17. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

    Text Solution

    |

  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  19. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

    Text Solution

    |

  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |