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Instructions
In each of these questions two equations numbered I and II are given. You have to solve both the equations and –
Give answer a: if x < y
Give answer b: if x ≤ y
Give answer c: if x > y
Give answer d: if x ≥ y
Give answer e: if x = y or the relationship cannot be established.
Solution
I.$$x^{2} + 13x + 42 = 0$$
=> $$x^2 + 7x + 6x + 42 = 0$$
=> $$x (x + 7) + 6 (x + 7) = 0$$
=> $$(x + 7) (x + 6) = 0$$
=> $$x = -7 , -6$$
II.$$y^{2} + 19y + 90 = 0$$
=> $$y^2 + 9y + 10y + 90 = 0$$
=> $$y (y + 9) + 10 (y + 9) = 0$$
=> $$(y + 9) (y + 10) = 0$$
=> $$y = -9 , -10$$
$$\therefore x > y$$
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