Let a , b and c be three real numbers satisfying [ array lll a & b & c array ] [ array…
Mathematics · JEE Advanced · NTA Exams — Complex Numbers and Quadratic Equations
Let a, b and c be three real numbers satisfying
\[\left[\begin{array}{lll} a & b & c \end{array}\right]\left[\begin{array}{lll} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \end{array}\right]=\left[\begin{array}{lll} 0 & 0 & 0 \end{array}\right]\]......(E)
Let b = 6, with a and c satisfying (E). If α and β are the roots of the quadratic equation ax2 + bx + c = 0, then \(\sum_{n=0}^{\infty}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)^{n}\) is
\[\left[\begin{array}{lll} a & b & c \end{array}\right]\left[\begin{array}{lll} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \end{array}\right]=\left[\begin{array}{lll} 0 & 0 & 0 \end{array}\right]\]......(E)
Let b = 6, with a and c satisfying (E). If α and β are the roots of the quadratic equation ax2 + bx + c = 0, then \(\sum_{n=0}^{\infty}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)^{n}\) is
- 6
- 7
- 6/7
- ∞
Answer
(C) 6/7
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