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Descartes' Rule

The roots of ...

Question

The roots of equation $a x^{2} + b x + c = 0$ are $2, 7$ find $a, b, c$

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Solution

The roots of equation are $2, 7$
The sum of roots is given as $\frac{- b}{a} = 2 + 7 = 9$
The product of root is given by $\frac{c}{a} = 2 \times 7 = 14$
$⟹ a = 1, b = - 9, c = 14$

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