For the equation $ax^2+bx+c=0,$ $a,b$ and $c$ are real, Statement 1: If the equation $ax^2+bx+c=0, 0 < a < b < c$, has non-real complex roots $z_1$ and $z_2$, then $|z_1| > 1, |z_2| > 1$. Statement 2: Complex roots always occur in conjugate pairs.

Statement 2 is a fundamental theorem of algebra stating that non-real complex roots of polynomials with real coefficients always occur in conjugate pairs, making it true. For Statement 1, if the roots are z1 and z2, their product is |z1| * |z2| because they are conjugates, and by Vieta's formulas this product is c/a. Since the coefficients satisfy 0 < a < b < c, the ratio c/a is strictly greater than 1. Therefore, |z1|^2 > 1, which implies that both |z1| > 1 and |z2| > 1. This proves Statement 1 is true and Statement 2 is the correct explanation for Statement 1.

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