Find the values of $p$ and $q$ for which $\displaystyle x = \frac{2}{3}$ and $x = - 3$ are the roots of the equation $px^2 + 7x + q = 0$

By Vieta's formulas for the equation px squared plus 7x plus q equals 0, the sum of the roots is negative 7 over p and the product is q over p. The sum of the roots two thirds and negative 3 is negative 7 over 3, so negative 7 over p equals negative 7 over 3, which means p equals 3. The product of the roots is negative 2, so q over p equals negative 2, which gives q equals negative 6.

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