The equation x^2+px+q=0, q cannot be equal to 0, has two unequal roots such that the squares of the roots are the same as the two roots. Calculate the product pq.

Answer 1

there is only one number which satisfies "the square of itself is equal to itself": it is 1. (0 is also the other but it is stated that q cannot be equal to 0)
therefore,
(x-1)(x-1) = x^2 + 2x + 1
p = 2
q = 1

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