Question

find the roots of quadratic equation root 3 x square - 2 x minus root 3 is equal to zero

Answer 1

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Answer 2

Answer:

$\text{The solution is }x=\frac{1\pm\sqrt{1-\sqrt3}}{3}$

Step-by-step explanation:

Given the equation

$3x^2-2x-\sqrt3=0$

we have to find the roots of the given equation.

Comparing given equation with standard form of equation

$ax^2+bx+c=0$

$a=3, b=-2, c=\sqrt3$

By determinant formula

The solution is

$3x^2-2x-\sqrt3=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{2\pm\sqrt{(-2)^2-4(3)(\sqrt3)}}{2(3)}\\\\x=\frac{2\pm\sqrt{4-12\sqrt3}}{6}\\\\x=\frac{1\pm\sqrt{1-\sqrt3}}{3}\\\\\text{The solution is }x=\frac{1\pm\sqrt{1-\sqrt3}}{3}$