Find the roots of the quadratic equations by applying the quadratic formula.
(i) `2x^2 -7x+3 =0`
(ii) `2x^2+x-4 =0`
(iii) `4x^2+4sqrt3x+3=0`
(iv) `2x^2+x+4 = 0`

Explanation

To find the roots of the given quadratic equations using the quadratic formula, we will follow these steps for each equation. The quadratic formula is given by:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

where \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation \(ax^2 + bx + c = 0\).

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