Molar mass of \(\text{H}_3\text{PO}_4 = 98 \, \text{g/mol}\)
Mass of solution = \(1 \times 1000 \times 1.54 = 1540 \, \text{g}\)
Mass of \(\text{H}_3\text{PO}_4 = 0.7 \times 1540 = 1078 \, \text{g}\)
Moles of \(\text{H}_3\text{PO}_4 = \frac{1078}{98} = 11 \, \text{moles}\)
Thus, molarity = \(11 \, \text{M}\).
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: