Question

Solve the equation given below-
$3{x^2} - 6x + 2 = 0$

Answer 1

Hint: In order to solve given equation, we will use quadratic formula which states that if the quadratic equation is represented as $a{x^2} + bx + c = 0,$ then the solution will be given as
$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$

Complete step-by-step answer:
Given equation $3{x^2} - 6x + 2 = 0$
We know that if our quadratic equation is $a{x^2} + bx + c = 0,$then solution is $x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$
Here, $a = 3,b = - 6,c = 2$
By putting these values in the above formula, we get
\[
   \Rightarrow x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} \\
   \Rightarrow x = \dfrac{{ - ( - 6) \pm \sqrt {{{( - 6)}^2} - 4 \times 3 \times 2} }}{{2 \times 3}} \\
   \Rightarrow x = \dfrac{{6 \pm \sqrt {36 - 24} }}{6} \\
   \Rightarrow x = \dfrac{{6 \pm \sqrt {12} }}{6} \\
   \Rightarrow x = \dfrac{{6 \pm 2\sqrt3 }}{6} \\
   \Rightarrow x = 1 \pm \dfrac{1}{{\sqrt3 }} \\
\]
Hence, the solution of the given equation is \[x = 1 \pm \dfrac{1}{{\sqrt3 }}\]

Note: In order to solve these types of questions, remember the formula of solution of a quadratic equation. Sometimes these problems can also be solved by factorization. Also remember a quadratic equation can also be formed from its roots or when the sum of roots and products of roots of a quadratic equation is given.