JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\alpha\) and \(\beta\) are the roots of the equation \(2 x (2 x +1)=1,\) then \(\beta\) is equal to
- A \(2 \alpha^{2}\)
- B \(2 \alpha(\alpha+1)\)
- C \(-2 \alpha(\alpha+1)\)
- D \(2 \alpha(\alpha-1)\)
Answer & Solution
Correct Answer
(C) \(-2 \alpha(\alpha+1)\)
Step-by-step Solution
Detailed explanation
\(\alpha\) and \(\beta\) are the roots of the equation \(4 x^{2}+2 x-1=0\) \(4 \alpha^{2}+2 \alpha=1 \Rightarrow \frac{1}{2}=2 \alpha^{2}+\alpha\) \(\beta=\frac{-1}{2}-\alpha\) using equation ( 1\()\) \(\beta=-\left(2 \alpha^{2}+\alpha\right)-\alpha\)…
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