The roots of the equation x^2 + bx - c = 0 wh | vedclass

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(C) Given the quadratic equation $x^2 + bx - c = 0$ with $b, c > 0$.Let the roots of the equation be $\alpha$ and $\beta$.According to the properties

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Of opposite sign

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(C) Given the quadratic equation $x^2 + bx - c = 0$ with $b, c > 0$.Let the roots of the equation be $\alpha$ and $\beta$.According to the properties of quadratic equations,the sum of the roots is $\alpha + \beta = -b$ and the product of the roots is $\alpha \beta = -c$.Since $b > 0$,it follows that $\alpha + \beta = -b Since $c > 0$,it follows that $\alpha \beta = -c If the product of the roots $(\alpha \beta)$ is negative,it implies that one root must be positive and the other must be negative.Therefore,the roots are of opposite sign.

The roots of the equation $x^2 + bx - c = 0$ where $b, c > 0$ are:

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