Question

what is the splitting term of x^2-3x-1​

Answer 1

${ \bold{ \boxed{ \boxed{ \huge\red {ANSWER}}}}}$

${ \bold{ \underline{Given \: \: function} : - }} \\ \\ { \bold{ \pink{ : \implies {x}^{2} - 3x - 1 = 0 }}} \\ \\ { \bold{ \underline{To \: \: find} : - }} \\ { \bold{ \mathtt{ \pink{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: splitting \: \: term}}}}$

${ \bold{ \boxed{ \huge \red{ \mathtt{ \bigstar \: solution}}}}}$

${ \bold{ \orange{ : \implies \: {x}^{2} - 3x - 1 = 0}}} \\ \\ { \bold{ \orange{ : \implies \: {x}^{2} - (3x) - 1 = 0 }}} \\ \\ { \bold{ \orange{ : \implies \: {x}^{2} + ( \frac{ \sqrt{13} - 3}{2} )x \: - ( \frac{ \sqrt{13} + 3}{2}) x - 1 = 0 }}} \\ \\ { \bold{ \orange{ : \implies \:(x - \frac{ 3 + \sqrt{13} }{2} )(x - \frac{3 - \sqrt{13} }{2} ) = 0 }}} \\ \\ { \bold{ \orange{ : \implies \: x = \frac{3 + \sqrt{13} }{2} \: \: and \: \: x = \frac{3 - \sqrt{13} }{2} }}}$