Home
Class 11
MATHS
If alpha, beta be the roots of the equat...

If `alpha, beta` be the roots of the equation `4x^(2)-16x+c=0, c epsilonR` such that `1lt alpha lt 2` and `2 lt beta lt 3`, then the number of integral values of c are

A

5

B

6

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
Let `f(x) = 4x^(2) - 16x + c`.
Clearly, 1 and 3 lie outside the roots and 2 lies between the roots.
`therefore" "f(1) gt 0, f(2) lt 0 and f(3) gt 0`
`rArr" "c-12 gt 0 and c-16 lt 0 rArr 12 lt c lt 16 rArr c = 13, 14, 15`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|22 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|138 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta be the roots of 4x^(8) - 16x + c = 0, c in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 , then the number of integral values of c is

If alpha, beta be the roots of 4x^2-17x+lambda=0, lambda in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 then the number of integral values of lambda is

If alpha and beta are the roots of the equation x^(2)+alpha x+beta=0 such that alpha ne beta , then the number of integral values of x satisfying ||x-beta|-alpha|lt1 is

If alpha, beta are the roots of the equation x^(2)+alphax + beta = 0 such that alpha ne beta and ||x-beta|-alpha|| lt alpha , then

If alpha,beta(alpha lt beta) are the real roots of equation x^2-(k+4)x+k^2-12=0 such theta 4 in (alpha,beta) , then the number of integral value of k is equal to

If alpha and beta are the roots of the equation x^(2)-px +16=0 , such that alpha^(2)+beta^(2)=9 , then the value of p is

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

If alpha, beta are the roots of the equation ax^2 + bx +c=0 then the value of (1+alpha+alpha^2)(1+beta+beta^2) is

If alpha and beta (alpha lt beta) are the roots of the equation x^(2) + bx + c = 0 , where c lt 0 lt b , then

If c lt a lt b lt d , then roots of the equation bx^(2)+(1-b(c+d)x+bcd-a=0

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Section I - Solved Mcqs
  1. If both roots of the quadratic equation x^(2)-2ax+a^(2)-1=0 lie in (-2...

    Text Solution

    |

  2. If .^(6)C(k) + 2* .^(6)C(k+1) + .^(6)C(k+2) gt .^(8)C(3) then the quad...

    Text Solution

    |

  3. If alpha, beta be the roots of the equation 4x^(2)-16x+c=0, c epsilonR...

    Text Solution

    |

  4. Let f(x) = x^(3) + 3x^(2) + 9x + 6 sin x then roots of the equation (1...

    Text Solution

    |

  5. The number of integral values of a for which x^(2) - (a-1) x+3 = 0 has...

    Text Solution

    |

  6. If 1 lies between the roots of equation y^2 - my +1 = 0 and [x] denote...

    Text Solution

    |

  7. If a ,b ,c ,d are four consecutive terms of an increasing A.P., then t...

    Text Solution

    |

  8. If ax^(2)+bx+c=0, a ne 0, a, b, c in R has distinct real roots in (1,2...

    Text Solution

    |

  9. If the equation ax^(2) + bx + 6 = 0 has real roots, where a in R, b in...

    Text Solution

    |

  10. If a and b are distinct positive real numbers such that a, a(1), a(2),...

    Text Solution

    |

  11. The roots of ax^(2) +bx +c =0 " whose " a ne 0, b ,c in R , " are non...

    Text Solution

    |

  12. If alpha and beta are non-real, then condition for x^(2) + alpha x + b...

    Text Solution

    |

  13. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  14. If a, b in R, then the equation x^(2) - abx - a^(2) = 0 has

    Text Solution

    |

  15. The set of real values of a for which the equation x^(2) = a(x+a) has ...

    Text Solution

    |

  16. If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roo...

    Text Solution

    |

  17. if cos^4x+sin^2x-p=0 has real solutions then

    Text Solution

    |

  18. If a. 3^(tanx) + a. 3^(-tanx) - 2 = 0 has real solutions, x != pi/2 , ...

    Text Solution

    |

  19. If a, b are the real roots of x^(2) + px + 1 = 0 and c, d are the real...

    Text Solution

    |

  20. If a and 4a + 3b + 2c have same sign. Then, ax^(2) + bx + c = 0(a ne 0...

    Text Solution

    |