Home
Class 12
MATHS
Find the number of roots of the equation...

Find the number of roots of the equation `e^(x) = sqrt (-x)`.

Text Solution

Verified by Experts

To find the number of roots of the equation `e^(x) = sqrt(-x)` ,we draw the graphs of `y = e^(x) and y = sqrt (-x)` and check the number of points of intersection.

From the figure, there is only one point of intersection, hence only one root `x_(0)`.
Promotional Banner

Topper's Solved these Questions

  • GRAPHS OF ELEMENTARY FUNCTIONS

    CENGAGE PUBLICATION|Exercise EXERCISES|34 Videos

  • GRAPHS OF POLYNOMIAL AND RATIONAL FUNCTIONS

    CENGAGE PUBLICATION|Exercise Exercises|17 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Exercises|22 Videos

Similar Questions

Explore conceptually related problems

Find the number of roots of the equation xlog_(e)x= 1 .

The number of roots of the equation x^2+5x+6=0 is

Find the number of solution of the equation 1+e^(cot^2x)=sqrt(2|sinx|-1)+(1-cos2x)/(1+sin^4x) for x in (0,5pi)dot

Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0.

Find the number of roots of the equation tan(x+pi/6)=2tanx ,forx in (0,3pi)dot

Draw the graph of y=x^(3)-x^(2)+x-2 and find the number of real root(s) of the equation x^(3)-x^(2)+x-2=0 . Also locate the root.

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

The number of roots of the equation is x^2 -7x+12=0

Consider the graph of y = f(x) as shown in the following figure. (i) Find the sum of the roots of the equation f (x) = 0. (ii) Find the product of the roots of the equation f(x) = 4. (iii) Find the absolute value of the difference of the roots of the equation f(x) = x+2 .

Find the roots of the equation x+1/x=3

CENGAGE PUBLICATION-GRAPHS OF ELEMENTARY FUNCTIONS -EXERCISES
  1. Find the number of roots of the equation e^(x) = sqrt (-x).

    Text Solution

    |

  2. Draw the graph of y= (1)/((1//x)).

    Text Solution

    |

  3. (a) Draw the graph of f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",,...

    Text Solution

    |

  4. Sketch the regions which points satisfy |x+y| ge 2.

    Text Solution

    |

  5. Sketch the region satisfying |x| lt |y|.

    Text Solution

    |

  6. For a point P in the plane, let d1(P)a n dd2(P) be the distances of th...

    Text Solution

    |

  7. Draw the graph of y= (x-1)/(x-2).

    Text Solution

    |

  8. The following figure shows the graph of f(x) =ax^(2)+bx +c, then find ...

    Text Solution

    |

  9. The entire graphs of the equation y=x^2+kx-x+9 is strictly above the x...

    Text Solution

    |

  10. If x^2+2a x+a<0AAx in [1,2], the find the values of adot

    Text Solution

    |

  11. Draw the graph of f(x) = x|x|.

    Text Solution

    |

  12. Draw the graph of the function: Solve |(x^2)/(x-1)|lt=1 using the grap...

    Text Solution

    |

  13. Draw the graph of y = |x^(2) - 2x|-x.

    Text Solution

    |

  14. Draw the graph of y = {{:(2^(x)",",, x^(2)-2x le 0 ),( 1+3.5 x- x^(2),...

    Text Solution

    |

  15. Draw the graph of f(x)= |2x-1|+ |2x-3|. Find the range of the function...

    Text Solution

    |

  16. Draw the graph of f(x) =y= |x-1|+3|x-2|-5|x-4| and find the values of ...

    Text Solution

    |

  17. Find the set of real value(s) of a for which the equation |2x+3|+2x-3|...

    Text Solution

    |

  18. Draw the graph of y= 2^(((|x|+x))/(x)).

    Text Solution

    |

  19. Draw the graph of y= x ^((1)/(log(e)x)).

    Text Solution

    |

  20. Find the number of solutions to the equation x+log(e)x=0.

    Text Solution

    |

  21. draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

    Text Solution

    |