21
The entire graph of the function f(x) = x2 + kx - x + 9 is strictly above the x-axis if and only if
y = x2 + (k- 1) x + 9 = (x + (k -1)/2)2 - ((k- 1)/2) + 9
For the entire graph to lie above the x-axis. y should be greater than 0, for all x.
So, 9 - ((k- 1)/2) 2 > 0 i.e., (k - 7) (k + 5) < 0 or - 5 < k < 7
The determinant given above = (2, 1, 6)
It gives the three equations, b - 3 c = 2; c - a = 1; 3a - b = 6.
This system of equations, has no solution as using the second equation in the third gives b - 3c = -3, which contradicts the first.
B32 is
