If two quadratic equations px² + px + 4 = 0 and x² + qx + q = 0 have a common root 2, then what is p + q equal to?

Question

Accepted Answer

−2. Substituting x = 2 in first: 4p + 2p + 4 = 0 → 6p = −4 → p = −2/3. In second: 4 + 2q + q = 0 → 3q = −4 → q = −4/3. Then p + q = −2/3 − 4/3 = −6/3 = −2.

If two quadratic equations px² + px + 4 = 0 and x² + qx + q = 0 have a common root 2, then what is p + q equal to?

Explanation

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