Home
Class 12
MATHS
The number of roots of the equation x^2+...

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

A

2

B

4

C

zero

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of the hyperbola is
`(x^(2))/(9)-(y^(2))/(16)=1`
The equation of the tangent is
`y=mx+sqrt(9x^(2)-16)`
`"or sqrt(9m^(2)-16)=2sqrt5`
`"or "m= pm2`
or a + b = sum of roots = 0
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWERS TYPE|18 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMOREHENSION TYPE|21 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.6|4 Videos

  • HIGHT AND DISTANCE

    CENGAGE PUBLICATION|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

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

State which of the following is the sum of the roots of the equation 3x^2-5x+7=0 ?

The sum of the roots of the equation x^3 + 5x + 1 = 0 is

If the sum of the roots of the equation 2x^2+ax+6=0 be 5, then which of the following is the value of a ?

The roots of the equation x^(2)+x-6=0 are

The number of solutions for the equations x^(2) -5 |x| +6 =0 is-

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.

Sum of the roots of equation x^2-6x+2=0 is

CENGAGE PUBLICATION-HYPERBOLA-EXERCISES
  1. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

    Text Solution

    |

  2. A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a t...

    Text Solution

    |

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

    Text Solution

    |

  4. The locus of a point whose chord of contact with respect to the circle...

    Text Solution

    |

  5. The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the...

    Text Solution

    |

  6. The number of possible tangents which can be drawn to the curve 4x^2-9...

    Text Solution

    |

  7. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 pa...

    Text Solution

    |

  8. Locus of the feet of the perpendiculars drawn from either foci on a va...

    Text Solution

    |

  9. P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, and N...

    Text Solution

    |

  10. The coordinates of a point on the hyperbola (x^2)/(24)-(y^2)/(18)=1 wh...

    Text Solution

    |

  11. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 me...

    Text Solution

    |

  12. The locus of a point, from where the tangents to the rectangular hyp...

    Text Solution

    |

  13. If tangents P Qa n dP R are drawn from a variable point P to thehyperb...

    Text Solution

    |

  14. The number of points on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 from w...

    Text Solution

    |

  15. If a ray of light incident along the line 3x+(5-4sqrt(2))y=15 gets ref...

    Text Solution

    |

  16. The chord of contact of a point P w.r.t a hyperbola and its auxiliary ...

    Text Solution

    |

  17. The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at r...

    Text Solution

    |

  18. The locus of the point which is such that the chord of contact of ta...

    Text Solution

    |

  19. If x=9 is the chord of contact of the hyperbola x^2-y^2=9 then the equ...

    Text Solution

    |

  20. If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2...

    Text Solution

    |