if a an integer , a belongs to [ - 5 , 0] then probability that the graph of the function
y = 2x^2 + 4(a+1)x - 8a - 14 = 0 is strictly above the x - axis , is ..
ANSWER IS 1 /6 . i need proper method.
y = 2x^2 + 4(a+1)x - 8a - 14 = 0 is strictly above the x - axis , is ..
ANSWER IS 1 /6 . i need proper method.
-
2x^2 + 4(a+1)x - 8a - 14 = 0
or, x^2 + 2(a+1)x - 2a - 7 = 0
or, x^2 + 2x- 7 = 0 [putting a=0]
or, (x+1)^2=8
putting 0, it turns to be (x+1)^2=8 which is a parabola and will always remain above the x-axis
putting the negative values, equations that are formed are also of parabola but of reverse direction which will always stay under the x-axis.
thus the probability makes 1/6
or, x^2 + 2(a+1)x - 2a - 7 = 0
or, x^2 + 2x- 7 = 0 [putting a=0]
or, (x+1)^2=8
putting 0, it turns to be (x+1)^2=8 which is a parabola and will always remain above the x-axis
putting the negative values, equations that are formed are also of parabola but of reverse direction which will always stay under the x-axis.
thus the probability makes 1/6