Home
Class 12
MATHS
The number of real solutions of the equa...

The number of real solutions of the equation `(9//10)^x=-3+x-x^2` is

A

2

B

0

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
2
Let `f(x) = -3 + x - x^(2)`. Then `f(x) lt 0` for all x, because coefficient of `x^(2)` is negative and `D lt 0`. Thus, L.H.S. of the given equation is always positive, whereas the R.H.S. is always less than zero.
Hence, there is no solution.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|38 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Linked Comprechension Type|37 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.13|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

The number of real solution of the equation e^x=x is

The number of real solutions of the equation (sinx-x)(cosx-x^2)=0 is

The number of real solutions of the equation sin (e^x)=2^x+2^(-x) is

The number of real solutions of the equation (sinx-x)(cosx-x^2)=0 is__

The number of real solutions of the equation (sinx-x)(cosx-x^(2))=0 is

The number of the real solutions of the equation x^2-3absx+2=0 is

The number of real solution to the equation -x^2+x-1=sin^(2)x

The number of real solution of the equation tan^(-1) sqrt(x^2-3x +2) + cos^(-1) sqrt(4x-x^2 - 3) = pi is

Find the number of real solutions to the equation 3cos^(-1)x-pix-pi/2=0

The number of solutions of the equation sin(e^x)=5^x+5^(-x) is

CENGAGE PUBLICATION-THEORY OF EQUATIONS-Single Correct Answer Type : Exercise
  1. The total number of integral values of a so that x^2-(a+1)x+a-1=0 has ...

    Text Solution

    |

  2. The number of integral values of a for which the quadratic equation (x...

    Text Solution

    |

  3. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is

    Text Solution

    |

  4. The number of real solutions of |x|+2sqrt(5-4x-x^2)=16 is/are

    Text Solution

    |

  5. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  6. If alpha,beta,gamma,sigma are the roots of the equation x^4+4x^3-6x^2+...

    Text Solution

    |

  7. If (mr ,1/mr) where r=1,2,3,4, are four pairs of values of x and y ...

    Text Solution

    |

  8. If roots of an equation x^n-1=0a r e1,a1,2, a(n-1), then the value of...

    Text Solution

    |

  9. If tantheta1,tantheta2,tantheta3 are the real roots of the x^2-(a+1x^2...

    Text Solution

    |

  10. If alpha,beta,gamma are the roots of x^3-x^2-1=0 then the value of (1+...

    Text Solution

    |

  11. If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3K x^2...

    Text Solution

    |

  12. Set of all real value of a such that f(x)=((2a-1)x^2+2(a+1)x+(2a-1))/(...

    Text Solution

    |

  13. If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imagi...

    Text Solution

    |

  14. If the expression [m x-1+(1//x)] is non-negative for all positive real...

    Text Solution

    |

  15. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

    Text Solution

    |

  16. Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(...

    Text Solution

    |

  17. Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R. T...

    Text Solution

    |

  18. Let f(x)=a x^2+bx +c a ,b ,c in R. If f(x) takes real values for re...

    Text Solution

    |

  19. If both roots of the equation a x^2+x+c-a=0 are imaginary and c > -1, ...

    Text Solution

    |

  20. If (b^2-4a c)^2(1+4a^2)<64 a^2, a<0 , then maximum value of quadratic ...

    Text Solution

    |