Home
Class 12
MATHS
If (a, 0) is a point on a diameter of th...

If (a, 0) is a point on a diameter of the circle `x^2+y^2=4` then `x^2 -4x- a^2=0` has A) Exactly one real root in `(-1, 0]` B) Exactly one real root in `[2, 5]` C) Distinct roots greater than `-1` D) Distinct roots less than `5 `

A

Exactly one ral root in `[-1,0]`

B

Exactly one real root in `[2,5]`

C

Distinct roots greater than `-1`

D

Distinct roots less than 5

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

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

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|1 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise -5 : Subjective Type problems|12 Videos

  • SEQUENCE AND SERIES

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

Similar Questions

Explore conceptually related problems

Let f(x)= 3/(x-2)+4/(x-3)+5/(x-4) . Then f(x)=0 has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

If the equation x^(2)-2ax+a^(2)+a-3=0 has exactly one real root in (1,3) then largest integral value of a is

Prove that the equation x^(3) + x – 1 = 0 has exactly one real root.

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

If the equaion x^(2) + ax+ b = 0 has distinct real roots and x^(2) + a|x| +b = 0 has only one real root, then

x^(3)+ax^(2)-bx-4=0 has (A) at least one negative root (C) one positive and one nell real roots 2 all real roots 2

The smallest integral value of a for which the equation x^(3)-x^(2)+ax-a=0 have exactly one real root,is

If f(x) is continuous in [0,2] and f(0)=f(2) then the equation f(x)=f(x+1) has (A) one real root in [0,2](B) atleast one real root in [0,1](C) atmost one real root in [0,2](D) atmost one real root in [1,2]

The equation e^(sin x)-e^(-sin x)-4=0 has (A) infinite number of real roots (B) no real roots (C) exactly one real root (D) exactly four real roots

VIKAS GUPTA (BLACK BOOK)-QUADRATIC EQUATIONS -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. if allvalues of x which satisfies the inequality log ((1//3))(x ^(2) +...

    Text Solution

    |

  2. Which of the following statement(s) is/are correct ?

    Text Solution

    |

  3. If (a, 0) is a point on a diameter of the circle x^2+y^2=4 then x^2...

    Text Solution

    |

  4. Let x^2-px+q=0, where p in R,q in R have the roots alpha,beta such tha...

    Text Solution

    |

  5. If a,b,c are rational numbers (a gt b gt c gt 0) and quadratic equatio...

    Text Solution

    |

  6. For the quadratic polynomial f (x) =4x ^(2)-8ax+a. the statements (s) ...

    Text Solution

    |

  7. Given a,b, c are three distinct real numbers satisfying the inequality...

    Text Solution

    |

  8. Let f (x) =x ^(2) -4x +c AA x in R, where c is a real constant, then w...

    Text Solution

    |

  9. If 0 lt a lt b lt c and the roots alpha, beta of the equation ax ^(2)...

    Text Solution

    |

  10. If satisfies |x-1| + |x-2|+|x-3|gt6, then :

    Text Solution

    |

  11. If both roots of the quadratic equation ax ^(2)+x+b-a =0 are non real ...

    Text Solution

    |

  12. If a,b are two numbers such that a ^(2) +b^(2) =7 and a ^(3) + b^(3) =...

    Text Solution

    |

  13. The number of non-negative integral ordered pair (s) (x,y) for which ...

    Text Solution

    |

  14. If alpha, beta, gamma and delta are the roots of the equation x ^(4) -...

    Text Solution

    |

  15. The value of 'k' for which roots of the equation 4x^2-2x+k=0 are comp...

    Text Solution

    |

  16. If a,b,c in R, then for which of the following graphs of the quadrati...

    Text Solution

    |

  17. a, b, c, in R, a ne 0 and the quadratic equation ax^(2) + bx + c = 0 h...

    Text Solution

    |

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

    Text Solution

    |

  19. The equation cos ^(2) x - sin x+lamda = 0, x in (0, pi//2) has roots t...

    Text Solution

    |

  20. If the equation ln (x^(2) +5x ) -ln (x+a +3)=0 has exactly one solutio...

    Text Solution

    |