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In these questions, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer.
Give answer :
(1) If x < y
(2) If x > y
(3) If x ≤ y
(4) If x ≥ y
(5) If relationship between x and y cannot be determined
I. 15x^2 - 11x + 2 =0
To find the roots of this equation use the formula x1 = (-b +√(b^2 - 4ac))/2a ; substitute a = 15, b = -11, c = 2 we get x1 = 2/5 = 0.4
Similarly to find the another root x2 = (-b -√(b^2 - 4ac))/2a; we get x2 = 1/3 =0.33
(x1, x2) = (0.4, 0.33)
II. 10y^2 - 9y + 2 =0
Similarly using the above formula we find the roots for 10y^2 - 9y + 2 =0 (a = 10, b = -9, c = 2)
(y1, y2) = (0.5, 0.4)
Comparing the roots (x1, x2) = (0.4, 0.33) with y1 =0.5
clearly y1 is greater than both x1 and x2.
Now compare the roots (x1, x2) with y2 = 0.4
Here we can observe x1 = y2 = 0.4
but x2<y2 i.e.,0.33<0.4
In all cases x<y except one case where x=y. So the answer should be x ≤ y.
Hence option 'C'.
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