Advanced MathVery hardFactoring a quartic as a quadratic in x squared
Advanced Math practice question
For all values of x, x⁴ − 5x² + 4 = (x² − a)(x² − b), where a and b are constants with a < b. What is the value of b − a?
Answer: 3
Treating x² as the variable: the factors of 4 that add to 5 are 1 and 4, so a = 1, b = 4, and b − a = 3.
Common wrong answers
- If you answered 4
- 4 is b alone.
- If you answered 5
- 5 is a + b.
- If you answered -3
- −3 subtracts in the wrong order.
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