Home
Class 12
MATHS
The equation (x^2+x=1)^2+1=(x^2+x+1)(x^2...

The equation `(x^2+x=1)^2+1=(x^2+x+1)(x^2-x-5)` for `x in (-2,3)` will have number of solutions. `1` b. `2` c. `3` d. 0

A

1

B

2

C

3

D

zero

Text Solution

Verified by Experts

The correct Answer is:
4
`(x^(2) + x + 1)^(2) + 1 = (x^(2) + x + 1) (x^(2) - x - 5)`
Since `x^(2) + x + 1 gt 0 AA x in R,`
Dividing both sides by `x^(2) + x + 1`, we get
`(x^(2) + x + 1) + (1)/((x^(2) + x + 1)) = x^(2) - x - 5`
`therefore L.H.S. ge 2`
But `x^(2) - x - 5 lt 1` for `x in (-2, 3)`
Therefore, the equation has 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

Find the number of solutions of equation (2x-3)2^x=1

For the equation cos^(-1)x+cos^(-1)2x+pi=0 , the number of real solution is (A)1 (B) 2 (C) 0 (D) oo

Solve the equations : ((x+1)^(3)-(x-1)^(3))/((x+1)^(2)-(x-1)^(2))=2

If the equation x^3+b x^2+c x+1=0,(b (a) -pi (b) -pi/2 (c) pi/2 (d) pi

If (2x^2-3x+1)(2x^2+5x+1)=9x^2 ,then equation has

The equation abs(x+1) abs(x-1)=a^2-2a-3 can have real solutions for x if 'a' belongs to

The set of real values of a for which the equation (2a^(2)+x^(2))/(a^(3)-x^(3))-(2x)/(ax+a^(2)+x^(2))+(1)/(x-a)=0 has a unique solution is (a) (−∞,1) (b) (−1,∞) (c) (-1,1) (d) R−{0}

The solutions of the equation |(x,2,-1),(2,5,x),(-1,2,x)|=0 are -

If (x^(3))/((2x-1) (x+2) (x-3))=A+ (B)/(2x-1) +(C )/(x+2) + (D)/(x-3), then the value of A is-

The equation (x+3-4(x-1)^(1//2))^(1//2)+(x+8-6(x-1)^(1//2))^(1//2)=1 has (A) no solution (B) only 1 solution (C) only 2 solutions (D) more than 2 solutions

CENGAGE PUBLICATION-THEORY OF EQUATIONS-Single Correct Answer Type : Exercise
  1. The number of value of k for which [x^2-(k-2)x+k^2]xx""[x^2+k x+(2k-1)...

    Text Solution

    |

  2. The sum of the values of x satisfying the equation (31+8sqrt(15))^(x^(...

    Text Solution

    |

  3. The equation (x^2+x=1)^2+1=(x^2+x+1)(x^2-x-5) for x in (-2,3) will hav...

    Text Solution

    |

  4. If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n...

    Text Solution

    |

  5. If P(x) is a polynomial with integer coefficients such that for 4 dist...

    Text Solution

    |

  6. Let f(x)=x^2+b x+c ,w h e r eb ,c in Rdot If f(x) is a factor of both...

    Text Solution

    |

  7. Consider the equation x^2+2x-n=0w h e r en in Na n dn in [5,100]dot T...

    Text Solution

    |

  8. The total number of integral values of a so that x^2-(a+1)x+a-1=0 has ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |