Algebra

[Shreya Nair]

[Saumik Karfa]

Let $a,b,c$ are the roots of the polynomial $x^3+Ax^2+Bx+C$.

then by vieta's formula

$a+b+c=-A \text{>} 0 \Rightarrow A \text{<} 0$

$ab+bc+ca=B \text{>} 0$

$abc= -C \text{>} 0 \Rightarrow C \text{<} 0$

Let $a$ is negative

$a^3+Aa^2+Ba+C$ is negative, contradiction.

then $a$ must be positive, similarly $b,c$ are positive.

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