Question

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

Answer 1

Answer:

Step-by-step explanation:

$\frac{1}{3}$ x² - √11 x + 1 = 0

D = b² - 4ac = (- √11)² - 4( $\frac{1}{3}$ ) (1) = 11 - 1$\frac{1}{3}$ = 9$\frac{3}{4}$ = $\frac{39}{4}$ = ( $\frac{\sqrt{39} }{2}$ )²

$x_{12}$ = $\frac{1}{2a}$ ( - b ± √D )

$x_{1}$ = $\frac{3}{2}$ ( √11 - $\frac{\sqrt{39} }{2}$ ) = $\frac{3\sqrt{11} }{2}$ - $\frac{3\sqrt{39} }{4}$ = $\frac{3}{4}$ ( 2√11 - √39 )

$x_{2}$ = $\frac{3}{4}$ ( 2√11 + √39 )