Given the polynomial [math]f(x)=x^n+a_1x^{n-1}+a_2x^{n-2}+...+a_n[/math], with real coefficients, and [math]{a_1}^{2}\lt a_2[/math], how can you show that not all roots of the equation [math]f(x)=0[/math] can be real?
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