If p(\neq 0) and q(\neq 0) are the roots of the equation x^{2}+px+q=0, then what is p^{2}+q^{2} equal to ?

Explanation

Sum of roots p+q = -p \implies q = -2p. Product of roots pq = q. Since q \neq 0, dividing by q gives p = 1. Substituting p=1 gives q = -2. Thus, p^2+q^2 = 1^2 + (-2)^2 = 5.

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