Relationship of roots and coefficients of a quadratic

The roots in polynomials are closely linked to the coefficients of that polynomial.

Sum of roots

If $p$ and $q$ are roots of $ax^2+bx+c=0$, then $p+q=-\frac ba$.

This means that the sum of roots of a quadratic is equal to $-\frac ba$.

Product of roots

If $p$ and $q$ are roots of $ax^2+bx+c=0$, then $p\times q=\frac ca$ (positive).

Evaluating other expressions

The equation $7x^2-2x+1=0$ has roots $p$ and $q$. Evaluate $\frac1p+\frac1q$

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