Advanced MathHardSum of all real solutions of a cubic
Advanced Math practice question
If x³ = 9x, what is the sum of all real solutions to the equation?
Answer: 0
Move everything to one side and factor: x³ − 9x = x(x² − 9) = x(x − 3)(x + 3) = 0. The solutions are 0, 3 and −3, which sum to 0. (Dividing by x would have lost the solution x = 0.)
Common wrong answers
- If you answered 3
- 3 is only the positive solution; −3 and 0 are solutions too.
- If you answered 6
- 6 adds 3 and 3, missing that one root is −3.
- If you answered 9
- 9 is the coefficient in the equation, not a sum of solutions.
More Advanced Math questions
- Hard
A population of bacteria doubles every 3 hours. If it starts at 500, which function models the population P af… - Hard
How many real solutions does x² + 4x + 5 = 0 have? - Hard
A car worth $20,000 loses 15% of its value each year. What is its value after 2 years? - Hard
An investment of $1,000 grows at 6% per year, compounded annually. Which expression gives its value after t ye… - Hard
If f(x) = x² − 1 and g(x) = x + 2, what is g(f(3))? - Hard
The parabola y = x² − 8x + 12 crosses the x-axis at two points. What is the x-coordinate of the vertex?
Not affiliated with the College Board. SAT is a trademark of the College Board.