1.

Which of the following pair of graphs intersect ? (i) y = x^(2) - xand y = 1 (ii) y = x^(2) - 2x+ 3 and y = sin x (iii) = x^(2) - x + 1 and y = x - 4

Answer»

Solution :Graphs`y = X^(2) - x` and y = 1 intersect when `x^(2) `- x and y = 1 intersect when `x^(2)- x = 1 or x^(2) = x -1 = 0 `
CLEARLY, this EQUATION has real solution. So graphs intersect.
Graphs `y = x^(2) - 2x + 3` and y = sin x intersect when `x^(2)-2x + 3 = sin x(x-1)^(2)+ 2 = sin` x, which is not possible as L.H.S. has least value 2, whereas R.H.S. has maximun value 1. So, Graphs do not intersect.
(iii) Graphs `y = x^(2)-x + 1` and y = x -4` intersect if `x^(2)-x + 1 = x - 4 or x^(2) = 2x + 5 = 0 or (x -1)^(2)+ 4 = 0`.
Clearly. this equation has non-real ROOTS . So, graphs do not intersect


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