Advanced MathHardCounting the distinct real zeros of a polynomial
Advanced Math practice question
How many distinct real values of x satisfy 2x³ − 6x² + 4x = 0?
Answer: 3
Factor: 2x(x² − 3x + 2) = 2x(x − 1)(x − 2) = 0. The zeros are 0, 1, and 2: three distinct values.
Common wrong answers
- If you answered 0
- 0 is one of the zeros, not the count.
- If you answered 1
- 1 counts only one zero.
- If you answered 2
- 2 forgets the zero at x = 0 from the common factor.
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.