Question
Given that $\alpha, \gamma$ are roots of the equation $A x^{2}-4 x+1=0$ and $\beta, \delta$ are roots of the equation $B x^{2}-6 x+1=0$. If $\alpha, \beta, \gamma$ and $\delta$ are in H.P., then(A) $A=5$(B) $A=-3$(C) $B=8$(D) $B=-8$
Step 1
P.). This means that their reciprocals are in Arithmetic Progression (A.P.). Let's denote the common difference of this A.P. as $d$. Then we have: \begin{align*} \beta &= \alpha + d, \\ \gamma &= \alpha + 2d, \\ \delta &= \alpha + 3d. \end{align*} Show more…
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