Home
Class 12
MATHS
If a, b, c are real then (b-x)^(2)-4(a-x...

If a, b, c are real then `(b-x)^(2)-4(a-x) (c-x)=0` will have always roots which are

A

real and equal

B

real and distinct

C

imaginary

D

both 1 and 2

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS & EXPRESSIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|88 Videos

  • QUADRATIC EQUATIONS & EXPRESSIONS

    AAKASH SERIES|Exercise EXERCISE-I|56 Videos

  • PROBABILITY

    AAKASH SERIES|Exercise Practise Exercise|165 Videos

  • RANDOM VARIABLE

    AAKASH SERIES|Exercise PRACTICE EXERCISE|34 Videos

Similar Questions

Explore conceptually related problems

IF x,a,b,c are real and (x-a+b^2)+(x-b+c)^2=0 then a,b,c are in

Prove that the roots of (x-a)(x-b)=h^(2) are always real.

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

IF the roots of (b-c) x^2+ (c-a) x+ (a-b) =0 are equal then a, b,c are in

The roots of the equation a ( b-c) x^2 -b(c-a) x+c(a-b)=0 are

IF C and D are the roots of (x-a) (x-b) -k=0 then the roots of (x-c) (x-d)+k=0 are

AAKASH SERIES-QUADRATIC EQUATIONS & EXPRESSIONS-EXERCISE-II
  1. For a, b, c in Q and b + c ne a, the roots of ax^(2)-(a+b+c)x+(b+c)=0

    Text Solution

    |

  2. For a, b, c in R and a, b, c are different, then the roots of (x+a)(x+...

    Text Solution

    |

  3. If a, b, c are real then (b-x)^(2)-4(a-x) (c-x)=0 will have always roo...

    Text Solution

    |

  4. If a, b, c are all positive and in H.P., then the roots of ax^(2)+2bx+...

    Text Solution

    |

  5. The root of (x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0, a in R are alw...

    Text Solution

    |

  6. Let f(x)=x^(2)+ax+b, where a, b in R. If f(x)=0 has all its roots imag...

    Text Solution

    |

  7. The roots of ax^(2) + 2bx + c = 0 and bx^(2)- 2sqrt(ac)x+b=0 are simu...

    Text Solution

    |

  8. If a in Z and the equation (x-a)(x-10) +1=0 has integral root...

    Text Solution

    |

  9. If the roots of (1)/(x+a)+ (1)/(x+b)= (1)/(c) are equal in magnitude ...

    Text Solution

    |

  10. If (x + 2)(x + 3b) = c has roots alpha,beta , then the roots of (x + a...

    Text Solution

    |

  11. IF 20 ^(3- 2x^2 = ( 40 sqrt(5) ) ^(3x^2-2), then x=

    Text Solution

    |

  12. {x in R: |x-2|= x^(2)}=

    Text Solution

    |

  13. The equation |2x - x^(2) - 3|=1 has

    Text Solution

    |

  14. If |x^(2)| + |x| + 12 = 0, then x =

    Text Solution

    |

  15. The number of real roots of |x^(2)| - 5|x| + 6 = 0 is

    Text Solution

    |

  16. sqrt((x)/(x-3))+ sqrt((x-3)/(x))= (5)/(2), x ne 0, x ne 3 then x=

    Text Solution

    |

  17. If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 ...

    Text Solution

    |

  18. The number of solutions of the equation |x^2|-3|x|+2=0 is

    Text Solution

    |

  19. The number of real roots of 3^(2x^(2)-7x+7)= 9 is

    Text Solution

    |

  20. The equation e^(sin x)-e^(-sin x)-4=0 has

    Text Solution

    |