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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.
Solution
I : $$3p^2 + 17p + 10 = 0$$
=> $$3p^2 + 15p + 2p + 10 = 0$$
=> $$3p (p + 5) + 2 (p + 5) = 0$$
=> $$(3p + 2) (p + 5) = 0$$
=> $$p = \frac{-2}{3} , -5$$
II : $$10q^2 + 9q + 2 = 0$$
=> $$10q^2 + 5q + 4q + 2 = 0$$
=> $$5q (2q + 1) + 2 (2q + 1) = 0$$
=> $$(5q + 2) (2q + 1) = 0$$
=> $$q = \frac{-2}{5} , \frac{-1}{2}$$
$$\therefore p < q$$
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