The standard form of √3 - 12x + 13x^2 is 13x^2 - 12x√3 + 3, obtained by rearranging terms and rationalizing the square root term.
The given expression is √3 - 12x + 13x^2. To convert this quadratic expression into standard form, we rearrange the terms so that the powers of x are in descending order. The standard form of a quadratic expression is usually written as ax^2 + bx + c, where a, b, and c are constants.
Starting with √3 - 12x + 13x^2, we can rewrite it as 13x^2 - 12x + √3. Now, to make it a standard quadratic expression, we need to express the term with the square root as a constant. This involves rationalizing the expression by multiplying both the numerator and denominator of the square root term by its conjugate, which is √3.
This results in the expression (13x^2 - 12x√3 + 3), where the square root is eliminated from the denominator. Therefore, the standard form of the given expression is 13x^2 - 12x√3 + 3.
In summary, the standard form of the expression √3 - 12x + 13x^2 is 13x^2 - 12x√3 + 3, achieved by rearranging terms and rationalizing the square root term.