If two quadratic equations px^{2}+px+4=0 and x^{2}+qx+q=0 have a common root 2, then what is p+q equal to ?

Explanation

Substitute x=2 into the first equation: 4p+2p+4=0 \implies 6p=-4 \implies p=-2/3. Substitute x=2 into the second equation: 4+2q+q=0 \implies 3q=-4 \implies q=-4/3. Therefore, p+q = -2/3 - 4/3 = -6/3 = -2.

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