Home
Class 12
MATHS
If ax^(2) + bx + c = 0 , a , b, c in ...

If `ax^(2) + bx + c = 0 , a , b, c in` R has no real roots, and if
` c lt ` 0, the which of the following is ture ?
(a) a` lt` 0 (b) a + b + c gt 0` (c) ` a gt ` 0

A

`a(a-b+c)gt 0`

B

`c (a-b +c) gt 0`

C

`b (a-b+c) gt 0`

D

`(a+b+c) (a-b+c) gt 0`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|42 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|23 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

If ax^(2) + bx + c = 0 , a , b, c in R has no real roots, and if c lt 0, the which of the following is ture ? (a) a lt 0 (b) a + b + c gt 0 (c) a +b +c lt 0

If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c< 0 , then which of the following is true?

If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c 0 (c) a >0

If the equation ax^(2) + bx + c = 0, a,b, c, in R have non -real roots, then

If ax^2+bx+c=0 and cx^2 + bx+a=0(a,b,c in R) have a common non-real roots, then which of the following is not true ?

If x^(2)+bx+x=0 has no real roots and a+b+c lt 0 then

If ax^(2)+bx+c = 0 has no real roots and a, b, c in R such that a + c gt 0 , then

If both roots of the quadratic equation ax ^(2)+x+b-a =0 are non real and b gt -1, then which of the following is/are correct ? (a) a gt 0 (b) a lt b (c) 3a gt 2+ 4b (d) 3a lt 2+ 4b

If the equation ax^2 + bx + c = 0, 0 < a < b < c, has non real complex roots z_1 and z_2 then

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?

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If ax^(2) + bx + c = 0 , a , b, c in R has no real roots, and if ...

    Text Solution

    |

  2. Let f (x) =ax ^(2) + bx+ c where a,b,c are integers. If sin ""pi/7. si...

    Text Solution

    |

  3. Let a, b, c, d be distinct integers such that the equation (x - a) (x ...

    Text Solution

    |

  4. Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=0--(1), w...

    Text Solution

    |

  5. The number of positive integral values of , m le 16 for which the equa...

    Text Solution

    |

  6. If the equation (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then...

    Text Solution

    |

  7. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

    Text Solution

    |

  8. The integral values of x for which x ^(2) + 17 x +7 is perfect square ...

    Text Solution

    |

  9. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

    Text Solution

    |

  10. The number of real values of 'a' for which the largest value of the fu...

    Text Solution

    |

  11. The number of all values of n, (whre n is a whole number ) for which t...

    Text Solution

    |

  12. The number of negative intergral values of m for which the expression ...

    Text Solution

    |

  13. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

    Text Solution

    |

  14. The smallest value of k for which both roots of the equation x^(2)-8kx...

    Text Solution

    |

  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  16. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

    Text Solution

    |

  17. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

    Text Solution

    |

  18. Find the number of integral vaues of 'a' for which the range of functi...

    Text Solution

    |

  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

    Text Solution

    |

  20. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  21. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

    Text Solution

    |