Advanced MathHardPerfect-square trinomial constant
Advanced Math practice question
For what value of c is x² + 10x + c a perfect square of a binomial?
Answer: 25
A perfect square (x + a)² = x² + 2ax + a². Here 2a = 10, so a = 5 and c = a² = 25.
Common wrong answers
- If you answered 5
- 5 is a, not a².
- If you answered 10
- 10 is the coefficient b, not c.
- If you answered 100
- 100 is 10², squaring the whole coefficient instead of half of 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.