Home
Class 12
MATHS
The entire graph of the equation y=x^2+k...

The entire graph of the equation `y=x^2+k x-x+9` in strictly above the `x-a xi s` if and only if `k<7` (b) `-5-5` (d) none of these

Text Solution

Verified by Experts

The correct Answer is:
`-5 lt k lt 7`

`y=x^(2)+(k-1)x+9=(x+(k-1)/(2))^(2)+9-((k-1)/(2))^(2)`
For entire graph to be above x-axis, we should have
`9-((k-1)/(2))^(2) gt 0`
`implies k^(2)-2k-35 lt 0`
`implies (k-7)(k+5) lt 0`
`implies -5 lt k lt 7`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.6|8 Videos
  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.7|5 Videos
  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.4|8 Videos
  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos
  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

The entire graph of the equation y=x^2+k x-x+9 in strictly above the x-axis if and only if (a) k -5 (d) none of these

The entire graph of the equation y=x^2+k x-x+9 in strictly above the x -axis if and only if (a) k<7 (b) -5 lt k lt 7 (c). k gt -5 (d) none of these

Knowledge Check

  • If the graphs of x^(2) = 4(y+9) and x + ky = 6 intersect on the x-axis , then k =

    A
    0
    B
    6
    C
    `-6`
    D
    any real number
  • Similar Questions

    Explore conceptually related problems

    The graph of the function y=16x^(2)+8(a+2)x-3a-2 is strictly above the x - axis, then number of integral velues of 'a' is

    The graph of the function y=16x^2+8(a+5)x-7a-5 is strictly above the x axis, then 'a' must satisfy the inequality

    The graph of the function y=16x^2+8(a+5)x-7a-5 is strictly above the x axis, then 'a' must satisfy the inequality

    The probability that the graph of y=16x^2 +8(a +5)x-7a-5=0, is strictly above the x-axis, If a in [-20,0]

    If a is an integer lying in [-5,30] , then the probability that the probability the graph of y=x^2+2(a+4)x-5a+64 is strictly above the x-axis is a. 1//6 b. 7//36 c. 2//9 d. 3//5

    The value of k for which the quadratic equation k x^2+1=k x+3x-11 x^2 has real and equal roots are (a) -11 ,-3, (b) 5,7 (c) 5,-7 (d) none of these

    If the point (2,\ -2) lies on the graph of the linear equation 5x+k y=4 , find the value of k