Find the roots of quad eq. 1\3x²-√11x+1=0 if they exist using quad formula​

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1. Answer:

   Step-by-step explanation:

   [tex]\frac{1}{3}[/tex] x² – √11 x + 1 = 0

   D = b² – 4ac = (- √11)² – 4( [tex]\frac{1}{3}[/tex] ) (1) = 11 – 1[tex]\frac{1}{3}[/tex] = 9[tex]\frac{3}{4}[/tex] = [tex]\frac{39}{4}[/tex] = ( [tex]\frac{\sqrt{39} }{2}[/tex] )²

   [tex]x_{12}[/tex] = [tex]\frac{1}{2a}[/tex] ( – b ± √D )

   [tex]x_{1}[/tex] = [tex]\frac{3}{2}[/tex] ( √11 – [tex]\frac{\sqrt{39} }{2}[/tex] ) = [tex]\frac{3\sqrt{11} }{2}[/tex] – [tex]\frac{3\sqrt{39} }{4}[/tex] = [tex]\frac{3}{4}[/tex] ( 2√11 – √39 )

   [tex]x_{2}[/tex] = [tex]\frac{3}{4}[/tex] ( 2√11 + √39 )

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