Question 1

Algebra Level 3

Let \( f(x), g(x), h(x)\) be quadratic polynomials having positive leading coefficient, each one having real and distinct zeros. If each pair of \(f(x), g(x)\) and \( h(x)\) has a common linear factor of \(x\), then the roots of the equation \( f(x) + 2g(x) + 3h(x) = 0 \):

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