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Can the equation have a positive root: (x+5)(x+6)+9=0

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3 votes

Answer:

no

Explanation:

In expanded form, the equation is ...

x^2 +11x +39 = 0

The discriminant is ...

11^2 -4(1)(39) = -35

It is negative, so there are only complex roots.

_____

Descartes' rule of signs tells you there are zero positive real roots, because there are zero sign changes in the coefficients.

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