Advanced MathHardSum of the squares of a quadratic's roots
Advanced Math practice question
The equation x² − 2x − 8 = 0 has roots p and q. What is the value of p² + q²?
Answer: 20
The roots are 4 and −2 (from (x − 4)(x + 2)), so p² + q² = 16 + 4 = 20. (Or (p + q)² − 2pq = 4 + 16 = 20.)
Common wrong answers
- If you answered 2
- 2 is p + q.
- If you answered 4
- 4 is (p + q)², forgetting the −2pq term.
- If you answered -12
- −12 adds 2pq instead of subtracting it.
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.