Home
Class 12
MATHS
Suppose a, b, c, d in R and 2ac = b + d...

Suppose `a, b, c, d in R and 2ac = b + d. ` Consider the quadratic equations `x^2+ 2ax + b = 0 and x^(2) + 2cx + d = 0` . Then

A

none of these equations have real roots

B

both the equations have real roots

C

exactly one of the equation has real roots

D

at least one of the equation has real roots

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Solved Examples (Numerical Answer Type Questions)|18 Videos
  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Exercise (Concept-based single correct answer type questions)|20 Videos
  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Solved Examples (Level 1 ( Single Correct Answer Type Questions)|80 Videos
  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|25 Videos
  • SETS, RELATIONS AND FUNCTIONS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEAR.S B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|19 Videos

Similar Questions

Explore conceptually related problems

In the quadratic equation 4x^(2) - 2 ( a + c - 1) x + ac - b = 0 (a gt b gt c)

If the quadratic equation ax^(2)+2cx+b=0 and ax^(2)+2bx+c=0(b!=c) have a common root,then a+4b+4c=

Let a,b,c,d be distinct real numbers and a and b are the roots of the quadratic equation x^(2)-2cx-5d=0. If c and d are the roots of the quadratic equation x^(2)-2ax-5b=0 then find the numerical value of a+b+c+d

Roots of the quadratic eauation of the type (ax + b) (cx + d) = 0 are given by the linear equations ax + b = 0 and cx + d = 0. Find roots of 16x^(2) - 9 = 0 .

If a,b,c are integers and b^(2)=4(ac+5d^(2)),dcN, then roots of the quadratic equation ax^(2)+bx+c=0 are

The abscissae and ordinates of the points A and B are the roots of the equations x^(2)+2ax+b=0 and x^(2)+2cx+d=0 respectively,then the equation of circle with AB as diameter is

If a,b,c d in R such that (a+2c)/(b+3d) +4/3=0, then the equation ax ^(3) + bx^(3)+ cx+d =0 has

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

MCGROW HILL PUBLICATION-QUADRATIC EQUATIONS-Solved Examples (Level 2 (Straight Objective Type Questions))
  1. Suppose a, b, c, d in R and 2ac = b + d. Consider the quadratic equa...

    Text Solution

    |

  2. If the roots of the equation (1)/(x+a) + (1)/(x+b) = (1)/(c) are equal...

    Text Solution

    |

  3. If a,b are the roots of x^2 - 10cx-11d = 0 and c,d are roods of x^2- 1...

    Text Solution

    |

  4. If alpha and beta are the roots of the equation ax^2 + bx + c = 0, the...

    Text Solution

    |

  5. Suppose a in I and the equation (x - a) (x - 5) = 3 has integral roots...

    Text Solution

    |

  6. If the ratio of the roots of x^2 + bx + c =0 and x^2 + qx + r = 0 is ...

    Text Solution

    |

  7. If a and b(!=0) are the roots of the equation x^2+ax+b=0 then the leas...

    Text Solution

    |

  8. If a + b + c = 0 then the quadratic equation 3ax^(2) + 2bx + c = 0 has

    Text Solution

    |

  9. If a lt b lt c lt d, then the eqution 3(x - a) (x - c) + 5 (x - b) (x ...

    Text Solution

    |

  10. For real x , the function (x-a)(x-b)//(x-c) will assume all real value...

    Text Solution

    |

  11. Let a, b, c be real numbers, a != 0. If alpha is a zero of a^2 x^2+bx...

    Text Solution

    |

  12. If alpha and beta are the ral roots of x ^(2) + px +q =0 and alpha ^(4...

    Text Solution

    |

  13. The equation x^((3)/4 (log2x)^2+log2 x -(5)/(4))=sqrt(2) has :

    Text Solution

    |

  14. Let f(x) be a quadratic expression which is positive for all ral x and...

    Text Solution

    |

  15. If alpha , beta are the roots of the quadratic equation ax^(2) + bx ...

    Text Solution

    |

  16. If a, b, c in R and the equations ax^(2) + bx + c = 0 and x^(3) + 3x ...

    Text Solution

    |

  17. Let a, b, c be non-zero real numbers such that ; int0^1 (1 + cos^8 x)(...

    Text Solution

    |

  18. The number of real solutions of the equation 27^(1//x)+12^(1//x)=2.8...

    Text Solution

    |

  19. lf 0 < a < b < c < d, then the quadratic equation ax^2 + ...

    Text Solution

    |

  20. If the equation ax^(2) + 2 bx - 3c = 0 has no real roots and (3c)/(4) ...

    Text Solution

    |