Question

t square minus 15 fingers the relationship between zeros of the coefficients
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Answer 1

${t}^{2} - 15 = 0 \\ t = + \sqrt{15 \: } \: \: \: \: or \: \ - \sqrt{15}$

Answer 2

$Let \: p(t) \: be \: the \: given \: polynomial \\ \\ p(t) = t {}^{2} - 15 = (t + \sqrt{15})(t - \sqrt{15} ) \\ \\ Now ,\\ p(t) = 0 \\ \\ = > (t + \sqrt{15} )(t - \sqrt{15} ) = 0 \\ \\ = > t = - \sqrt{15} \: or \: \sqrt{15 } \\ \\ = > \alpha = - \sqrt{15} \: \: and \: \: \beta = \sqrt{15 } \\ \\ \\ Sum \: of \: zeros: \\ \alpha + \beta = - \sqrt{15} + \sqrt{15} = 0 \\ \\ Product \: of \: zeros :\\ \alpha \beta = - \sqrt{15} \times \sqrt{15} = - 15$