Question

Find the roots of the quadratic equation 3x²-2√6x+2 = 0 by using the quadratic formula.

Answer 1

for finding root of the equation we use two formule.

quadratic equation :

$ax {}^{2} + bx + c = 0$
............................................................................................

$x = (( - b) + \sqrt{d } ) \div 2a$
$x = ( ( - b) - \sqrt{d} ) \div 2a$
$d = b ^{2} - 4ac$
.............................................................................................

$given....$
a=3

b= -2√6

c=2

finding value of d....

$d = ( - 2 \sqrt{6} ) ^{2} - 4 \times 3 \times 2$
d=24-24=0

one more rule i tell you if d=0 then root of the equation(x) are equals....

you can check putting d =0 in both get same result....

$x = ( - ( - 2 \sqrt{6} ) + \sqrt{0} ) \div 2 \times 3 \\ \\ x = 2 \sqrt{6} \div 6 \\ \\ x = \sqrt{2 \times 3} \ \: \div 3 \\ \\ x \ = \sqrt{2} \div \sqrt{3}$