TS EAMCET · Maths · Quadratic Equation
If \(m_1\) and \(m_2\) are the roots of the equation \(x^2+(\sqrt{3}+2) x+(\sqrt{3}-1)=0,\) then the area of the triangle formed by the lines \(y=m_1 x, y=m_2 x\) and \(y=c\)
- A \(\left(\frac{\sqrt{33}-\sqrt{11}}{4}\right) \cdot c^2\)
- B \(\left(\frac{\sqrt{33}+\sqrt{11}}{4}\right) \cdot c^2\)
- C \(\left(\frac{\sqrt{11}-\sqrt{33}}{2}\right) \cdot c^2\)
- D \(\frac{\sqrt{33}}{2} \cdot c^2\)
Answer & Solution
Correct Answer
(B) \(\left(\frac{\sqrt{33}+\sqrt{11}}{4}\right) \cdot c^2\)
Step-by-step Solution
Detailed explanation
Since, \(m_1\) and \(m_2\) are the roots of the equation \(x^2+(\sqrt{3}+2) x+(\sqrt{3}-1)=0\) then \(\quad m_1+m_2=-(\sqrt{3}+2)\), \(m_1 m_2=\sqrt{3}-1\) \(\therefore m_1-m_2=\sqrt{\left(m_1+m_2\right)^2-4 m_1 m_2}\) \(=\sqrt{(3+4+4 \sqrt{3}-4 \sqrt{3}+4)}\) \(=\sqrt{11}\) and…
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