If the polynomial P(x) = x^3 - 7x^2 + 14x - 8 has known roots at 1 and 4, find the remaining root.
Answer and explanation
Correct answer: B. x = 2
- Step 1: By Vieta's relations, the sum of roots for x^3 - 7x^2 + 14x - 8 is 7. Step 2. Let the roots be 1, 4, and r. Step 3. Then 1 + 4 + r = 7 => 5 + r = 7 => r = 2. Answer: x = 2. Why not the others: r = -2 gives sum 3; r = 3 gives sum 8; r = 5 gives sum 10.
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