Advanced MathHardChecking a radical equation for a true value
Advanced Math practice question
Which value of x makes the equation √(x + 4) = x − 2 a true statement?
- A. 5Correct
- B. 0
- C. 2
- D. −4
Answer: A. 5
√9 = 3 = 5 − 2. Squaring gives x² − 5x = 0, and x = 0 fails the check because √4 = 2 but 0 − 2 = −2.
Why the other answers are wrong
- B. 0
- 0 is the extraneous root: √4 = 2, but 0 − 2 = −2.
- C. 2
- 2 gives √6 on the left and 0 on the right.
- D. −4
- −4 gives 0 on the left and −6 on the right.
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.