Home
Class 12
MATHS
The quadratic equation, a (x -b)(x-c) + ...

The quadratic equation, `a (x -b)(x-c) + b (x-c)(x-a) + c (x-a) (x-b)=0`, : where `0 ltaltbltc` have a) exactly one root lying betwen a and b b) exactly one root lying between b and c C) exactly one root lying between a and c D) both roots lying between a and c

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are equal then

both roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are

If the roots of the quadratic equation (a-b) x^(2) + (b - c) x + (c - a) =0 are equal , prove that b +c = 2a

Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

The roots of the quadratic equation (a+b-2c)x^(2)+(2a-b-c)x+(a-2b+c)=0 are

If the quadratic equation4x^2-2(a+c-1)x+a c-b=0(a > b > c) (a)Both roots se greater than a (b)Both roots are less than c (c)Both roots lie between c/2 and a/2 (d)Exactly one of the roots lies between c/2 and a/2

RESONANCE DPP-JEE MAINS-All Questions
  1. If f(x)=2/sqrt3 tan^-1((2x+1)/sqrt3) -ln(x^2+x+1)+(k^2-5k+3)x+10 ...

    Text Solution

    |

  2. If the lines L1:2x-3y-6=0,L2: x+y-4=0 and L3: x+2 and tanA ,tanB an...

    Text Solution

    |

  3. The quadratic equation, a (x -b)(x-c) + b (x-c)(x-a) + c (x-a) (x-b)=0...

    Text Solution

    |

  4. If sintheta+sinvarphi=a and costhetavarphi+cosvarphi=b , then cos(...

    Text Solution

    |

  5. If y=x+e^x , then (d^2x)/(dy^2) is equal to

    Text Solution

    |

  6. Locus of the point of intersection of perpendicular tangents on the ...

    Text Solution

    |

  7. Range of function f(x)=a r ccot(2x-x^2), is [pi/4,(3pi)/3] (b) [0,pi/...

    Text Solution

    |

  8. A circle S of radius ' a ' is the director circle of another circle S1...

    Text Solution

    |

  9. If | vec a|=3,| vec b|=4 then a value of lambda for which vec a+lambd...

    Text Solution

    |

  10. Number of solutions of the equation 2^x+3^x+4^x-5^x=0 is 0 (b) 1 (c...

    Text Solution

    |

  11. if y=(A+Bx)e^(mx)+(m-1)^-1 e^x then (d^2y)/(dx^2)-2m(dy)/(dx)+m^2y is ...

    Text Solution

    |

  12. A pair of tangents are drawn to a unit circle with centre at the origi...

    Text Solution

    |

  13. Let alpha+ibeta;alpha,beta in R , be a root of the equation x^3+q x+r...

    Text Solution

    |

  14. Of f(x)=p x^2+q x+r is a quadratic expression such that [a^2a1b^2b1c^2...

    Text Solution

    |

  15. A rectangle ABCD is inscribed in a circle. Let PQ be the diameter of t...

    Text Solution

    |

  16. If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two str...

    Text Solution

    |

  17. If the lines a x+2y+1=0,b x+3y+1=0 and c x+4y+1=0 are concurrent, then...

    Text Solution

    |

  18. The equation to the circle which touches the axis of y at the origin a...

    Text Solution

    |

  19. 56. Match the interval(s) of x, for which fx) is real Column-4 Column-...

    Text Solution

    |

  20. Let f(theta)=1/(1+(tantheta)^(2013)) then value ofsum(theta=1^(@))^(8 ...

    Text Solution

    |