Answer:Answer is option C : [[tex]x^{2}[/tex] + 3x + 3 ] =0
Note: None of options matches with given question.
instead of "-3" , there should be "-[tex]\frac{3}{2}[/tex]".
Step-by-step explanation:
Note: None of options matches with given question.
instead of "-3" , there should be "[tex]\frac{3}{2}[/tex]".
Here, First thing you have to observe the nature of roots.
∴ x = -[tex]\frac{3}{2}[/tex]+[tex]\frac{\sqrt{3}}{2}[/tex]i and x = -[tex]\frac{3}{2}[/tex]-[tex]\frac{\sqrt{3}}{2}[/tex]
∴ [ x+([tex]\frac{3}{2}[/tex]-[tex]\frac{\sqrt{3}}{2}[/tex]i) ][ x+([tex]\frac{3}{2}[/tex]+[tex]\frac{\sqrt{3}}{2}[/tex]i) ]=0
∴ [ [tex]x^{2}[/tex] + x([tex]\frac{3}{2}[/tex]+[tex]\frac{\sqrt{3}}{2}[/tex]i)+ x([tex]\frac{3}{2}[/tex]-[tex]\frac{\sqrt{3}}{2}[/tex]i) + ([tex]\frac{3}{2}[/tex]-[tex]\frac{\sqrt{3}}{2}[/tex]i)([tex]\frac{3}{2}[/tex]+[tex]\frac{\sqrt{3}}{2}[/tex]i) ]=0
∴ [[tex]x^{2}[/tex] + [tex]\frac{3}{2}[/tex]x + [tex]\frac{\sqrt{3}}{2}[/tex]ix + [tex]\frac{3}{2}[/tex]x - [tex]\frac{\sqrt{3}}{2}[/tex]ix + (3-[tex]\frac{\sqrt{3}}{2}[/tex]i)(3+[tex]\frac{\sqrt{3}}{2}[/tex]i) ] =0
∴ [[tex]x^{2}[/tex] + 3x + ([tex]\frac{3}{2}[/tex]-[tex]\frac{\sqrt{3}}{2}[/tex]i)([tex]\frac{3}{2}[/tex]+[tex]\frac{\sqrt{3}}{2}[/tex]i) ] =0
∴ [[tex]x^{2}[/tex] + 3x + [tex]\frac{9}{4}[/tex] - ([tex]\frac{\sqrt{3}}{2}[/tex]i)([tex]\frac{\sqrt{3}}{2}[/tex]i) ] =0
∴ [[tex]x^{2}[/tex] + 3x + [tex]\frac{9}{4}[/tex] - ([tex]\frac{3}{4}[/tex]) [tex]i^{2}[/tex] ] =0
∴ [[tex]x^{2}[/tex] + 3x + [tex]\frac{9}{4}[/tex] + ([tex]\frac{3}{4}[/tex]) ] =0
∴ [[tex]x^{2}[/tex] + 3x + [tex]\frac{12}{4}[/tex] ] =0
∴ [[tex]x^{2}[/tex] + 3x + 3 ] =0
Thus, Answer is option C : [[tex]x^{2}[/tex] + 3x + 3 ] =0
