Home
Class 12
MATHS
If c>0 and 4a+c<2b then ax^2-bx+c=0 has ...

If `c>0` and `4a+c<2b` then `ax^2-bx+c=0` has a root win which one of the following intervals a)(0,2) b)(2,3) c)(3,4) d)(-2,0)

A

`(0,2)`

B

`(2,3)`

C

`(3,4)`

D

`(-2,0)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f ( c )= ax^(2) - bx + c`
`f(2) = 4a - 2b + c lt 0 " "` (given )
` f(0) = c gt 0 " "` (given)
So, we can see that sign of f(x) changes, when x changes from 0 t0 2, it has a root in the interval (0,2).
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    NDA PREVIOUS YEARS|Exercise MCQ|74 Videos

  • PROBABILITY AND PROBABILIYT DISTRIBUTION

    NDA PREVIOUS YEARS|Exercise Multiple Choice Question|213 Videos

Similar Questions

Explore conceptually related problems

If c gt0 and 4a+clt2b then ax^(2)-bx+c=0 has a root in the interval

If a+b+c=0 and a^(2)+b^(2)+c^(2)=1, then the value of a^(4)+b^(4)+c^(4) is

Let a=hati - hatj, b=hati + hatj + hatk and c be a vector such that a xx c + b=0 and a.c =4, then |c|^(2) is equal to .

If f and g are two real functions defined by f={(a,1)(b,0),(c,8),(0,4)} and g={(a,5),(c,-3),(b,6)(0,2)} then dom ((sqrt(g))/(f)) is

Sum of the squares of the distances from a point to (c,0) and (-c,0) is 4c^(2) .Its locus is

If a,b,c,in R and satisfy 3a+5b+15c=0, the equation ax^(4)+bx^(2)+c=0 has -

If the roots of 9x^(2) - 2x +7 = 0 are 2 more than the roots of ax^(2) + bx + c = 0 , then 4a - 2b + c can be

If the equation a x^2+b x+c=0(a >0) has two real roots alphaa n dbeta such that alphalt-2 and betagt2, then which of the following statements is/are true? (a)a-|b|+c<0 (b)clt0,b^2-4a cgt0 (c) 4a-2|b|+c<0 (d) 9a-3|b|+c<0

Let a= hat(i) - hat(j) , b=hat(i) + hat(j) + hat(k) and c be a vector such that axx c + b=0 " and " a. c =4, then |c|^(2) is equal to

NDA PREVIOUS YEARS-POLYNOMIAL,QUADRATIC EQUATION & INEQUALITIES-Math
  1. Let alpha and beta (a lt beta) " be the roots of the equation " x^(2...

    Text Solution

    |

  2. Let alpha and beta (a lt beta) " be the roots of the equation " x^(2...

    Text Solution

    |

  3. If c>0 and 4a+c<2b then ax^2-bx+c=0 has a root win which one of the fo...

    Text Solution

    |

  4. Let alpha and beta (a lt beta) " be the roots of the equation " x^(2...

    Text Solution

    |

  5. Let alpha and beta be the roots of equation x^2-(1-2a^2)x + (1-2a^2) ...

    Text Solution

    |

  6. Let alpha and beta be the roots of the equation x^(2) - ( 1 - 2a^(2)...

    Text Solution

    |

  7. What is the greatest value of the positive integer n satisfying the co...

    Text Solution

    |

  8. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  9. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  10. If the point (a,a) lies between the lines |x + y| = 2 , then which on...

    Text Solution

    |

  11. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  12. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  13. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  14. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  15. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  16. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  17. If |a| denotes the absolute value of an integar , then which of the fo...

    Text Solution

    |

  18. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  19. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |

  20. 2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation ...

    Text Solution

    |