Home
Class 12
MATHS
A quadratic equation f(x)=a x^2+b x+c=0(...

A quadratic equation `f(x)=a x^2+b x+c=0(a != 0)` has positive distinct roots reciprocal of each ether. Then

A

`f(1)=0`

B

`af(1)lt0`

C

`af(1)gt0`

D

Nothing can be said about a f (1)

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos
  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

A quadratic equation f(x)=ax^(2)+bx+c=0(a!=0) has positive distinct roots reciprocal of each ether. Then

If quadratic equation f(x)=x^(2)+ax+1=0 has two positive distinct roots then

If the equation x^(3)-3ax^(2)+3bx-c=0 has positive and distinct roots, then

Find all values of the parameter a for which the quadratic equation (a+1)x^(2)+2(a+1)x+a-2=0 (i) has two distinct roots. (ii) has no roots. (iii) has to equal roots.

Suppose a, b, c are real numbers, and each of the equations x^(2)+2ax+b^(2)=0 and x^(2)+2bx+c^(2)=0 has two distinct real roots. Then the equation x^(2)+2cx+a^(2)=0 has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots

Consider the quadratic equation (k^(2)-4)x^(2)-(14k+4)x+48=0 has two distinct positive integral roots,then The value of k is

The value of p for which the quadratic equation 2px^(2) + 6x + 5 = 0 has real and distinct roots is

Consider quadratic equations x^(2)-ax+b=0 and x^(2)+px+q=0 If the above equations have one common root and the other roots are reciprocals of each other, then (q-b)^(2) equals

RESONANCE-DPP-QUESTION
  1. If alpha,beta are the roots of the equation ax^2 + bx+c=0 then the roo...

    Text Solution

    |

  2. If ""(alpha)and (beta) are the roots of equation x^(2)-3x+1=0and a(n)=...

    Text Solution

    |

  3. A quadratic equation f(x)=a x^2+b x+c=0(a != 0) has positive distinct ...

    Text Solution

    |

  4. All the values of ' a ' for which the quadratic expression a x^2+(a-2)...

    Text Solution

    |

  5. If x^(2)+ax+10=0and x^(2)+bx-10=0 have common root, then a^(2)-b^(2) i...

    Text Solution

    |

  6. The least integral value of ' a ' for which the graphs y=2a x+1 and y=...

    Text Solution

    |

  7. If the quadratic equation alpha x^2 +beta x+a^2+b^2+c^2-ab-bc-ca=0 has...

    Text Solution

    |

  8. Let x=sqrt(3-sqrt5) and y=sqrt(3+sqrt5) If the value of the expression...

    Text Solution

    |

  9. If a gt b gt 0 are two real numbers, the value of, sqrt(ab+(a-b)sqrt(...

    Text Solution

    |

  10. Consider the equation log(5)[(2+sqrt5)^(x)+(sqrt5-2)^(x)]=1/2-log(1//5...

    Text Solution

    |

  11. lf sum of maximum and minimum value of y = log2(x^4+x^2+1) - log2 (x^4...

    Text Solution

    |

  12. Find the sum of all the real solution (s) to the equation (x+y)^(2)=(x...

    Text Solution

    |

  13. If x^2 + 2(a-1)x + a + 5 = 0 has real roots belonging to the interval ...

    Text Solution

    |

  14. lf alpha and beta are the roots of the equation x^2-ax + b = 0 and ...

    Text Solution

    |

  15. Let r,s and t be the roots of the equation, 8x^(3)+1001x+2008=0. The v...

    Text Solution

    |

  16. The set of all values of ' a ' for which the quadratic equation 3x^2+2...

    Text Solution

    |

  17. If b^(2)gt4ac then roots of equation ax^(4)+bx^(2)+c=0 are all real & ...

    Text Solution

    |

  18. If the tan theta and sec theta are rots of the equation ax^(2)+bx+cx=0...

    Text Solution

    |

  19. Consider a quadratic equation ax^(2)+bx+c=0"where"a,b,c inR and a ne 0...

    Text Solution

    |

  20. All the roots of x^(3)+ax^(2)+bx+c are positive integers greater than ...

    Text Solution

    |