Instructions

For the two given equations I and II.
Give answer a: if p is greater than q.
Give answer b: if p is smaller than q.
Give answer c: if p is equal to q.
Give answer d: if p is either equal to or greater than q.
Give answer e: if p is either equal to or smaller than q.

Question 96

I. $$p^2 + 5p + 6 = 0$$
II. $$q^2 + 3q + 2 = 0$$

Solution

I : $$p^2 + 5p + 6 = 0$$

=> $$p^2 + 3p + 2p + 6 = 0$$

=> $$p (p + 3) + 2 (p + 3) = 0$$

=> $$(p + 2) (p + 3) = 0$$

=> $$p = -2 , -3$$

II : $$q^2 + 3q + 2 = 0$$

=> $$q^2 + q + 2q + 2 = 0$$

=> $$q (q + 1) + 2 (q + 1) = 0$$

=> $$(q + 2) (q + 1) = 0$$

=> $$q = -2 , -1$$

$$\therefore p \leq q$$


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