Home
Class 11
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

0

B

1

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(x) = - 3 + x - x^(2)`. Then,
`f(x) lt 0` for all x, because coefficient of `x^(2) lt 0` and disc. `lt 0`.
Thus, LHS of the given equation is always positive whereas the RHS is always less than zero. Hence, the given equation has no solution.
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|22 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|138 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

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

The number of real solution of the equation e^(x)+x=0, is

The number of real solutions of the equation 1-x = [cosx] is

The number of real solution of the equation x^(2)=1-|x-5| is:

The number of real solutions of the equation x-sinx=0, is

The number of real solutions of the equation log_(0.5)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 sin(e^x)=2^x+2^(-x) is

The number of real solutions of the equation 3^(-|x|)-2^(|x|)=0 is:

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Section I - Solved Mcqs
  1. if alpha,beta be the roots of the equation (x-a)(x-b)+x=0(c ne0), then...

    Text Solution

    |

  2. The number of real roots of (6 - x)^(4) + (8 - x)^(4) = 16, is

    Text Solution

    |

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

    Text Solution

    |

  4. The set of values of a for which each on of the roots of x^(2) - 4ax +...

    Text Solution

    |

  5. If (a x^2+c)y+(a x^2+c )=0a n dx is a rational function of ya n da c ...

    Text Solution

    |

  6. If p ,q , in {1,2,3,4}, then find the number of equations of the form ...

    Text Solution

    |

  7. If alpha and beta(alpha lt beta) are the roots of the equation x^(2)+b...

    Text Solution

    |

  8. The roots of the equatiion (a+sqrt(b))^(x^(2)-15)+(a-sqrt(b))^(x^(2)-1...

    Text Solution

    |

  9. if (1+k)tan^2x-4tanx-1+k=0 has real roots tanx1 and tanx2 then

    Text Solution

    |

  10. The number of values of the pair (a, b) for which a(x+1)^2 + b(-x^2 – ...

    Text Solution

    |

  11. If b gt a, then the equation (x-a)(x-b)-1=0 has (a) Both roots in (a...

    Text Solution

    |

  12. Let alphaa n dbeta be the roots of x^2-x+p=0a n dgammaa n ddelta be th...

    Text Solution

    |

  13. Let f(x) = ax^(3) + 5x^(2) - bx + 1. If f(x) when divied by 2x + 1 lea...

    Text Solution

    |

  14. If a ,b ,c(a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0 ares rational.

    Text Solution

    |

  15. If a, b, c are in H.P., then the equation a(b-c) x^(2) + b(c-a)x+c(a-b...

    Text Solution

    |

  16. The number of value of k for which [x^2-(k-2)x+k^2]xx""[x^2+k x+(2k-1)...

    Text Solution

    |

  17. If the ratio of the roots of the equation ax^2+bx+c=0 is equal to rati...

    Text Solution

    |

  18. If a, b, c are positive and a = 2b + 3c, then roots of the equation ax...

    Text Solution

    |

  19. If a, b, c in R and the quadratic equation x^2 + (a + b) x + c = ...

    Text Solution

    |

  20. If both roots of the quadratic equation x^(2)-2ax+a^(2)-1=0 lie in (-2...

    Text Solution

    |