Home
Class 12
MATHS
lf 0 < a < b < c < d, then ...

lf ` 0 < a < b < c < d`, then the quadratic equation `ax^2 + [1-a(b+c)]x+abc-d=0` A) Real and distinct roots out of which one lies between c and d B) Real and distinct roots out of which one lies between a and b C) Real and distinct roots out of which one lies between b and c (D) non -real roots

A

Real and distinct roots out of which one lies between c and d

B

Real and distinct roots out of which one lies between a and b

C

Real and distinct roots out of which one lies between b and c

D

Non-real roots

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise Numerical value type of JEE Main|15 Videos
  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Main ( Archive )|20 Videos
  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advance ( Archive )|20 Videos
  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos
  • QUIZ

    VMC MODULES ENGLISH|Exercise MATHEMATICS|30 Videos

Similar Questions

Explore conceptually related problems

If a, b, c in R and the quadratic equation x^2 + (a + b) x + c = 0 has no real roots then

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

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

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?

If a lt b lt c lt d , then for any real non-zero lambda , the quadratic equation (x-a)(x-c)+lambda(x-b)(x-d)=0 ,has real roots for

If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 + bx + c = 0 are non-real complex numbers, then

If a, b, c, d in R such that a lt b lt c lt d, then roots of the equation (x-a)(x-c)+2(x-b)(x-d) = 0

The quadratic equation 2x^(2)-sqrt5x+1=0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots

Let f(x)=a x^3+b x^2+c x+d , a!=0 If x_1 and x_2 are the real and distinct roots of f prime(x)=0 then f(x)=0 will have three real and distinct roots if

If a, b, c ∈ R, a ≠ 0 and the quadratic equation ax^2 + bx + c = 0 has no real root, then show that (a + b + c) c > 0

VMC MODULES ENGLISH-QUADRATIC EQUATIONS & INEQUATIONS -LEVEL -2
  1. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

    Text Solution

    |

  2. If roots of ax^2+bx+c=0 are equal in magnitude but opposite in sign, t...

    Text Solution

    |

  3. If alpha ne beta but alpha^(2)= 5 alpha - 3 and beta ^(2)= 5 beta...

    Text Solution

    |

  4. lf 0 &lt; a &lt; b &lt; c &lt; d, then the quadratic equation ax^2 + ...

    Text Solution

    |

  5. If alpha,beta are the roots of the equation ax^2 + bx +c=0 such that b...

    Text Solution

    |

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

    Text Solution

    |

  7. Consider the equation |x^2-2x- 3|=m .m belongs to R .If the given equa...

    Text Solution

    |

  8. Consider the equation |x^2-2x- 3|=m .m belongs to R .If the given equa...

    Text Solution

    |

  9. Consider the equation |x^(2)-2x-3|=m , m in R . If the given equatio...

    Text Solution

    |

  10. Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in...

    Text Solution

    |

  11. Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in...

    Text Solution

    |

  12. If alpha, beta the roots of equation (k + 1 )x ^(2) -(20k +14) x + 91...

    Text Solution

    |

  13. If alpha, beta the roots of equation (k + 1 )x ^(2) -(20k +14) x + 91...

    Text Solution

    |

  14. Let f (x) =x ^(2) + bx + c AA xin R, (b,c, in R) attains its least va...

    Text Solution

    |

  15. Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least val...

    Text Solution

    |

  16. Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least val...

    Text Solution

    |

  17. Consider the equation log2 ^2 x- 4 log2 x- m^2 -2m-13=0,m in R.Let the...

    Text Solution

    |

  18. Consider the equation log (2)^(2) x -4 log (2)x-m^(2) -2m -13=0, m in ...

    Text Solution

    |

  19. The equation x ^(4) -2x ^(3) + 4x -1=0 has four distinct real roots x ...

    Text Solution

    |

  20. The equation x ^(4) -2x ^(3) + 4x -1=0 has four distinct real roots x ...

    Text Solution

    |