[tex] {n}^{2} - n - 56 = [/tex]
[tex](n - 8)(n + 7)[/tex]
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[tex]a {x}^{2} + bx + c = 0[/tex]
[tex]delta = {b}^{2} - 4ac[/tex]
[tex]x(1) = \frac{ - b + \sqrt{delta} }{2a} \\ [/tex]
[tex]x(2) = \frac{ - b - \sqrt{delta} }{2a} \\ [/tex]
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[tex] {n}^{2} - n - 56 = 0[/tex]
[tex]delta = ({ - 1})^{2} - 4(1)( - 56)[/tex]
[tex]delta = 1 + 224[/tex]
[tex]delta = 225[/tex]
Thus ;
[tex]n(1) = \frac{ - ( -1) + \sqrt{225} }{2 \times 1} \\ [/tex]
[tex]n(1) = \frac{1 + 15}{2} \\ [/tex]
[tex]n(1) = \frac{16}{2} \\ [/tex]
[tex]n(1) = 8[/tex]
And
[tex]n(2) = \frac{ - ( - 1) - \sqrt{225} }{2 \times 1} \\ [/tex]
[tex]n(2) = \frac{ 1 - 15}{2} \\ [/tex]
[tex]n(2) = - \frac{14}{2} \\ [/tex]
[tex]n(2) = - 7[/tex]
So
[tex]n(1) = 8[/tex]
[tex]n(1) - 8 = 0 \: \: \: (\alpha )[/tex]
[tex]n - 8 = 0 \: \: \: \: ( \alpha )[/tex]
And
[tex]n(2) = - 7[/tex]
[tex]n(2) + 7 = 0 \: \: \: \: \: ( \beta )[/tex]
[tex]n + 7 = 0 \: \: \: \: ( \beta )[/tex]
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[tex] \alpha \times \beta = [/tex]
[tex](n - 8)(n + 7)[/tex]
