Home
Class 12
MATHS
If alpha and beta (alpha lt beta) are th...

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

A

`0 lt alpha lt beta`

B

`alpha lt 0 lt beta lt |alpha|`

C

`alpha lt beta lt 0`

D

`alpha lt 0 lt |alpha|lt beta`

Text Solution

AI Generated Solution

To solve the problem step by step, we will analyze the given conditions and derive the necessary conclusions. ### Step 1: Understand the given equation and its roots We have the quadratic equation: \[ x^2 + bx + c = 0 \] where \(\alpha\) and \(\beta\) are the roots of the equation, with the condition that \(\alpha < \beta\).
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|11 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|10 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|17 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Three Dimensional Coordinate System Exercise 12 : Question Asked in Previous Years Exam|2 Videos

Similar Questions

Explore conceptually related problems

If alpha beta( alpha lt beta) are two distinct roots of the equation. ax^(2)+bx+c=0 , then

If alpha, beta (alpha lt beta) are the roots of the equation 6x^(2) + 11x + 3 = 0 , then which of the following are real ?

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

Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .

If alpha and beta are the roots of the equation ax ^(2) + bx + c=0,a,b, c in R , alpha ne 0 then which is (are) correct:

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 ax^2 + bx +c =0 (a != 0; a, b,c being different), then (1+ alpha + alpha^2) (1+ beta+ beta^2) =

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

If alpha, beta, gamma are the roots of the equation x^(3) + ax^(2) + bx + c = 0, "then" alpha^(-1) + beta^(-1) + gamma^(-1)=

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

ARIHANT MATHS ENGLISH-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If alpha and beta (alpha lt beta) are the roots of the equation x^(2) ...

    Text Solution

    |

  2. In the quadratic equation ax^2 + bx + c = 0. if delta = b^2-4ac and al...

    Text Solution

    |

  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

    Text Solution

    |

  4. If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c ...

    Text Solution

    |

  5. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

    Text Solution

    |

  6. If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are ...

    Text Solution

    |

  7. Let aa n db be the roots of the equation x^2-10 c x-11 d=0 and those o...

    Text Solution

    |

  8. Let a,b,c be the sides of a triangle. No two of them are equal and lam...

    Text Solution

    |

  9. All the values of m for whilch both the roots of the equation x^2-2m x...

    Text Solution

    |

  10. If the roots of the quadratic equation x^2+p x+q=0 are tan30^0a n dtan...

    Text Solution

    |

  11. Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2...

    Text Solution

    |

  12. If the difference between the roots of the equation x^2+a x+1=0 is les...

    Text Solution

    |

  13. Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots o...

    Text Solution

    |

  14. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

    Text Solution

    |

  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

    Text Solution

    |

  16. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

    Text Solution

    |

  17. The smallest value of k, for which both the roots of the equation, x^2...

    Text Solution

    |

  18. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

    Text Solution

    |

  19. Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...

    Text Solution

    |

  20. solve 0=1+2x+3x^2

    Text Solution

    |

  21. Find the roots of x^2-6x-2=0

    Text Solution

    |