Advanced MathHardConstant term from the sum and difference of roots
Advanced Math practice question
The equation x² − 6x + c = 0 has two real solutions that differ by 4, where c is a constant. What is the value of c?
Answer: 5
The solutions sum to 6 (from −(−6)) and differ by 4, so they are 5 and 1. Their product is c: 5 × 1 = 5.
Common wrong answers
- If you answered 8
- 8 gives solutions 2 and 4, which differ by 2.
- If you answered 9
- 9 would make the two solutions equal (both 3), not 4 apart.
- If you answered -5
- −5 has the wrong sign; the product of 5 and 1 is positive.
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