Let and . What is the sum of all values of for which ?
Answer and explanation
Correct answer: C. -6
- 6 forgets the negative sign in Vieta's formula ().
- confuses the product of roots with the sum of roots, with a sign flip.
- -3 neglects to divide by the leading coefficient when applying Vieta's formula ().
- confuses the product of roots with the sum of roots, with a sign flip.
- -3 neglects to divide by the leading coefficient when applying Vieta's formula ().
- Step 1: Evaluate both compositions: , and .
- Step 2: Set the expressions equal: .
- Step 3: Apply Vieta's formula to find the sum of the roots: .
Answer
-6.
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