Question

evalute x²+√3x +6 i need it urgent plz help me​

Answer 1

Step-by-step explanation:

${x}^{2} + \sqrt{3} x + 6i \\ = {x}^{2} + 2 \: ( \dfrac{ \sqrt{3} }{2} )x + 6i \\ = {x}^{2} + 2( \dfrac{ \sqrt{3} }{2} )x + { (\dfrac{ \sqrt{3} }{2}) }^{2} + 6i - { (\dfrac{ \sqrt{3} }{2} )}^{2} \\ = {(x + \dfrac{ \sqrt{3} }{2} )}^{2} + 6i - \dfrac{3}{4} \\ = {(x + \dfrac{ \sqrt{3} }{2} )}^{2} - {( \sqrt{ \dfrac{3}{4} - 6i } \: ) }^{2} \\ = (x + \dfrac{ \sqrt{3} }{2} + \sqrt{ \dfrac{3}{4} - 6i} ) \: (x + \dfrac{ \sqrt{3} }{2} - \sqrt{ \frac{3}{4} - 6i } )$