SAT Nonlinear equations in one variable and systems of equations in two variables Practice Question 19 (Hard)

Question bank / Nonlinear equations in one variable and systems of equations in two variables

Math · Advanced MathHard

If $a$ and $b$ are the solutions to the equation $3x^2 - 12x + 5 = 0$ , what is the value of $ab + a + b$ ?

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Answer: 17/3

For $px^2 + qx + r = 0$ , the sum of the solutions is $-\frac{q}{p}$ and the product is $\frac{r}{p}$ . Here $a + b = \frac{12}{3} = 4$ and $ab = \frac{5}{3}$ . So $ab + a + b = \frac{5}{3} + 4 = \frac{17}{3}$ .

Using $a + b = -4$ (forgetting the negative in $-\frac{q}{p}$ ) gives $-\frac{7}{3}$ .

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