What is the other root of f(x)=0?
For the following two (02) items: Let f(x)=ax^{2}+bx+c be a quadratic polynomial such that f(1)=f(4)=2. Further, 2 is a root of f(x)=0.
- A. 1
- B. 2
- C. 3 ✓
- D. Cannot be determined
Correct Answer: C. 3
Explanation
Since f(1) = f(4) = 2, the parabola is symmetric about the vertical line x = \frac{1+4}{2} = 2.5. The roots of f(x) = 0 must also be symmetric about x = 2.5. If one root is x_1 = 2, the other root x_2 must satisfy \frac{2+x_2}{2} = 2.5 \implies x_2 = 3.
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