Home
Class 14
MATHS
The quadratic equation x^(2) + bx + 4 =...

The quadratic equation `x^(2) + bx + 4 = 0` will have real roots if.

A

Only `b le - 4`

B

Only `b ge 4`

C

`-4 lt b lt 4`

D

`b le - 4, b ge 4`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    PUNEET DOGRA|Exercise PREV YEAR QUESTIONS|103 Videos

  • PROPERTIES OF TRIANGLES

    PUNEET DOGRA|Exercise PREV YEAR QUESTION|30 Videos

  • SEQUENCE AND SERIES

    PUNEET DOGRA|Exercise PREVIOUS YEAR QUESTIONS|88 Videos

Similar Questions

Explore conceptually related problems

For what values of 'a' does the quadratic equation x^(2) - ax + 1 = 0 not have real roots ?

Assertion : 4x^(2) - 12x + 9 = 0 has repeated roots. Reason : The quadratic equation ax^(2) + bx + c = 0 have repeated roots if D gt 0 .

For what values of k does the quadratic equation 4x^(2) - 12x - k =0 have no real roots ?

For what values of 'a' does the quadratic equation x^(2)-ax+1=0 not have real roots?

a, b, c, in R, a ne 0 and the quadratic equation ax^(2) + bx + c = 0 has no real roots, then which one of the following is not true?

Assertion : 3y^(2) + 17y - 30 = 0 have distinct roots. Reason : The quadratic equation ax^(2) + bx + c = 0 have distinct roots (real roots) is D gt 0 .

For what value of k the quadratic equation x ^(2) - kx +4 have real and equal roots ?

If the quadratic equation ax^(2)+bx+6=0 does not have real roots and b in R^(+), then prove that a>max{(b^(2))/(24),b-6}

For the quadratic equation 4x^(2)-7kx+2=0 to have real roots,which of the following is always true?

PUNEET DOGRA-QUADRATIC EQUATIONS-PREV YEAR QUESTIONS
  1. If alpha and beta are the roots the equations ax^(2) +bx + c = 0, wher...

    Text Solution

    |

  2. The roots of the equation 2a^(2) x^(2) - 2abx + b^(2) = 0. When a lt 0...

    Text Solution

    |

  3. The quadratic equation x^(2) + bx + 4 = 0 will have real roots if.

    Text Solution

    |

  4. If alpha and beta are the roots of the equation x^(2) -x + 2 =0, then ...

    Text Solution

    |

  5. What is the difference in the roots of the equation x^(2) - 10x + 9 = ...

    Text Solution

    |

  6. If alpha and beta are the roots of the equation ax^(2) + bx + b = 0. T...

    Text Solution

    |

  7. The roots of the equation x^(2) - 8x + 16 = 0.

    Text Solution

    |

  8. If a and b are rational and b is not perect square. Then the quadratic...

    Text Solution

    |

  9. How many real roots of the equations x^(2) + 3|x| +2 = 0 have ?

    Text Solution

    |

  10. If alpha and beta roots of the equation x^(2) + bx + c = 0 then what i...

    Text Solution

    |

  11. If x^(2) - 8 x + 1 = 0 , what is the value of ( x^(2) + (1)/( x^(2)...

    Text Solution

    |

  12. If 4^(x) - 6.2^(x) + 8 = 0 then the values of x are :

    Text Solution

    |

  13. If the roots of a quadratic equation ax^(2)+ bx +c = 0 are alpha and b...

    Text Solution

    |

  14. If the sum of the roots of a quadratic equation is 3 and the product i...

    Text Solution

    |

  15. What is the degree of the equation (1)/(x-3) = (1)/(x + 2) - (1)/(2) ?

    Text Solution

    |

  16. If the roots of the equation 3ax^(2) + 2bx + c = 0 are in the ratio 2...

    Text Solution

    |

  17. The area of a rectangle whose length is 5 more than twice its width is...

    Text Solution

    |

  18. If the roots of the quadratic equation 3x^(2) - 5x + p = 0 are real an...

    Text Solution

    |

  19. If the roots of a quadratic equation are m + n and m - n, then the qua...

    Text Solution

    |

  20. If alpha, beta are the roots of x^(2) + px -q = 0 and lambda, delta ar...

    Text Solution

    |