If one of the roots of the equation x^2 - 5x | vedclass

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(B) The given quadratic equation is $x^2 - 5x - 14 = 0$. Factoring the equation: $(x - 7)(x + 2) = 0$,so the roots are $x_1 = 7$ and $x_2 = -2$. Since

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$(\sqrt{65}, 0)$

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(B) The given quadratic equation is $x^2 - 5x - 14 = 0$. Factoring the equation: $(x - 7)(x + 2) = 0$,so the roots are $x_1 = 7$ and $x_2 = -2$. Since the length of an axis must be positive,we take the absolute value or consider the valid root. Given the context,let the semi-conjugate axis $b = 7$. The square of the other root is the semi-transverse axis $a = (-2)^2 = 4$. For the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,the distance of the focus from the center is $c = \sqrt{a^2 + b^2}$. Substituting the values: $c = \sqrt{4^2 + 7^2} = \sqrt{16 + 49} = \sqrt{65}$. Thus,the focus on the positive $x$-axis is $(\sqrt{65}, 0)$.

If one of the roots of the equation $x^2 - 5x - 14 = 0$ is the length of the semi-conjugate axis of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ and the square of the other root is the semi-transverse axis,then the focus of the hyperbola that lies on the positive $x$-axis is

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