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.

Answer 1

Correct Question

While playing in the 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 the polynomial $a t^{2} + 5t+3a$ is equal to their product, then find the value of $a$

Concept

This question is related to the Quadratic polynomial.

Let $\alpha$ and $\beta$ are the zeros or roots of the quadratic polynomial $f(x):ax^{2} +bx+c$, then, the sum of the roots or sum of zeros of the polynomial is  $\alpha +\beta =- \frac{b}{a}$ .

And then the product of Roots or product of zeros of a Quadratic Polynomial is  $\alpha \beta =\frac{c}{a}$

Given

We have given if the sum of zeroes of the polynomial $a t^{2} + 5t+3a$ is equal to their product.

To Find

We have to find the value of $a$

Solution

Let $a t^{2} + 5t+3a=0$

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

and product of zeros $=\frac{c}{a} =\frac{3a}{a} =3$

Also, the sum of zeros = product of zeros

So,  $-\frac{5}{a}=3$

⇒ $a=-\frac{5}{3}$

As a result, the value of $a$ in given quadratic polynomial is  $-\frac{5}{3}$

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Answer 2

Question:

While playing in the garden, Sahiba saw a honeycomb and asked her mother what is that. She replied that it: $\# 39$ is 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 a polynomial $a t^{2}+5 t+3 a$ is equal to their product, then find the value of $a_{2}$.

Answer:

The sum of zeros is equal to the product of the zeros,  

$\mathrm{a}=\frac{-5}{3}$.

Step-by-step explanation:

Given:

Sum of zeroes of a polynomial $a t^{2}+5 t+3 a=0$ is equal to their product.

To find:

The value of $a_{2}$.

Step 1

Sum of zeroes of a polynomial  

$a t^{2}+5 t+3 a=0$

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

Step 2

Product of zeros $=\frac{c}{a}=\frac{3 a}{a}=3$

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

Therefore, $\frac{-5}{a}=3$

$\Rightarrow \mathrm{a}=\frac{-5}{3}$

The sum of zeros is equal to the product of the zeros,  $\mathrm{a}=\frac{-5}{3}$.

#SPJ3