JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha_1, \alpha_2, \ldots, \alpha_7\) be the roots of the equation \(x^7+\) \(3 x^5-13 x^3-15 x=0\) and \(\left|\alpha_1\right| \geq\left|\alpha_2\right| \geq \ldots \geq\left|\alpha_7\right|\). Then \(\alpha_1 \alpha_2-\alpha_3 \alpha_4+\alpha_5 \alpha_6\) is equal to \(..................\).
- A \(9\)
- B \(8\)
- C \(7\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(9\)
Step-by-step Solution
Detailed explanation
Given equation can be rearranged as \(x\left(x^6+3 x^4-13 x^2-15\right)=0\) clearly \(x=0\) is one of the root and other part can be observed by replacing \(x ^2= t\) from which we have \(\quad t^3+3 t^2-13 t-15=0\) \(\Rightarrow \quad( t -3)\left( t ^2+6 t +5\right)=0\) So,…
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