While playing in garden, Sahiba saw a honeycomb and asked her mother what is that. She replied that it's a honeycomb made by honey bees to store honey. Also, she told her that the shape of the honeycomb formed is parabolic. The mathematical representation of the honeycomb structure is shown in the graph. Based on the above information, answer the question If the sum of zeroes of polynomial \( a t^{2}+5 t+3 a \) is equal to their product, then find the value of \( a \).

Question

While playing in garden, Sahiba saw a honeycomb and asked her mother what is that. She replied that it's a honeycomb made by honey bees to store honey. Also, she told her that the shape of the honeycomb formed is parabolic. The mathematical representation of the honeycomb structure is shown in the graph. Based on the above information, answer the question If the sum of zeroes of polynomial \( a t^{2}+5 t+3 a \) is equal to their product, then find the value of \( a \).

Answer 1

\(at^2 + 5t + 3a = 0\)

Sum of zeros \(=\frac{-b}{a} = \frac{-5}{a}\)

Product of zeros \(=\frac{c}{a} = \frac{3a}{a}=3\)

Given that sum of zeros is equal to the product of the zeros.

\(\therefore\) \(\frac{-5}{a} = 3\)

\(\Rightarrow\) a \(=\frac{-5}{3}.\)