Home
Class 12
MATHS
In the given figure, vertices of Delta A...

In the given figure, vertices of `Delta ABC` lie on `y = f(x) = ax^2 + bx + c.` The `DeltaABC` is right angled isosceles triangle whose hypotenuse `AC = 4sqrt2` units. Number of integral values of `k` for which one root of `f(x) = 0` is more than `k` and other less than `k`

A

6

B

4

C

5

D

7

Text Solution

Verified by Experts

The correct Answer is:
3
`f(x) = 0`
`rArr x^(2)//(2sqrt(2)) - 2sqrt(2) = 0` or `x = pm 2sqrt(2)`
Therefore, number of integral values of K for which for which k lies in `(-2sqrt(2), 2sqrt(2))` is 5.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Numerical)|43 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|38 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

Find the number of integral values of k for which the equation 7 cos x+5 sin x=2k+1 has at least one solution.

Find the number of positive integral values of k for which kx ^(2) +(k-3)x+1 lt 0 for atleast one positive x.

A right angled isosceles triangle is inscribed in the circle x^2 + y^2 -4x - 2y - 4 = 0 then length of its side is

The set of real values of k for which the lines x + 3y +1=0, kx + 2y-2=0 and 2x-y + 3 = 0 form a triangle is

Find the value of k for which the quadratic equation (k+4)x^(2) + (k+1)k+1=0 has equal roots

Let f(x)=ax^(2)+bx+c , a ne 0 , a , b , c in I . Suppose that f(1)=0 , 50 lt f(7) lt 60 and 70 lt f(8) lt 80 . Number of integral values of x for which f(x) lt 0 is

. The lines (a+b)x + (a-b) y-2ab=0, (a-b)x+(a+b)y-2ab = 0 and x+y=0 form an isosceles triangle whose vertical angle is

Let A(h, k), B (1, 1) and C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which 'k' can take is given by

If one root of x^3+2x^2+3x+k=0 is sum of the other two roots then find the value of k

All the values of m for which both roots of the equation x^(2)-2mx+m^(2)-1=0 are greater than -2 but less than 4, lie in the interval

CENGAGE-THEORY OF EQUATIONS-Exercise (Comprehension)
  1. In the given figure, vertices of Delta ABC lie on y = f(x) = ax^2 + bx...

    Text Solution

    |

  2. In the given figure, vertices of Delta ABC lie on y = f(x) = ax^2 + bx...

    Text Solution

    |

  3. In the given figure, vertices of Delta ABC lie on y = f(x) = ax^2 + bx...

    Text Solution

    |

  4. Let f(x) =4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x,a be any re...

    Text Solution

    |

  5. Let f(x) =4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x,a be any re...

    Text Solution

    |

  6. Let f(x) =4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x,a be any re...

    Text Solution

    |

  7. Consider the equaiton 2 + |x^(2) + 4x + 3|= m , m in R Set of all ...

    Text Solution

    |

  8. Consider the equaiton 2 + |x^(2) + 4x + 3| = m , m in R Set of all...

    Text Solution

    |

  9. Consider the equaiton 2 + |x^(2) + 4x + 3|= m , m in R Set of all v...

    Text Solution

    |

  10. Consider the quadratic equation ax^(2) - bx + c =0,a,b,c in N which ...

    Text Solution

    |

  11. Consider the quadratic equation ax^(2) - bx + c =0,a,b,c in N which ...

    Text Solution

    |

  12. Consider the quadratic equation ax^(2) - bx + c =0,a,b,c in N which h...

    Text Solution

    |

  13. Consider the inequation x^(2) + x + a - 9 lt 0 The values of the r...

    Text Solution

    |

  14. Consider the inequation x^(2) + x + a - 9 lt 0 The values of the re...

    Text Solution

    |

  15. Consider the inequation x^(2) + x + a - 9 lt 0 The value of the pa...

    Text Solution

    |

  16. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  17. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  18. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  19. (af(mu) lt 0) is the necessary and sufficient condition for a particu...

    Text Solution

    |

  20. (af(mu) lt 0) is the necessary and sufficient condition for a particu...

    Text Solution

    |