Let the roots of the required quadratic equation be α and β.
It is given that the A.M. of the roots is 8.
\[ \text{A.M.} = \frac{\alpha + \beta}{2} = 8 \]
∴ \( \alpha + \beta = 16 \) … (1)
It is also given that the G.M. of the roots is 5.
\[ \text{G.M.} = \sqrt{\alpha \beta} = 5 \]
Squaring both sides, we get
∴ \( \alpha \beta = 25 \) … (2)
The quadratic equation whose roots are α and β is given by:
\[ x^2 - (\alpha + \beta)x + \alpha \beta = 0 \]
Substituting the values from (1) and (2):
\[ x^2 - 16x + 25 = 0 \]
Thus, the required quadratic equation is
\[ x^2 - 16x + 25 = 0 \]
The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?