Roots , triangle and lines !!

Geometry Level 2

The area of the triangle formed by the lines \[y=m_1 \times x \]and \[y=m_2 \times x\] and \[y=c\] is \[\frac{c^{2}}{a} \times (\sqrt{b}+\sqrt{d})\],where c is constant not given and \[m_1\] & \[m_2\] are the roots of the equation \[x^{2} + (\sqrt{3} + 2)x + \sqrt{3}-1\]. Also a,b&d are integers ,what is the value of \[a+b+d\] .

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