Case study (4 Marks)

Question 14 Marks

Priya visited a temple in Gwalior. On the way she sees the Agra Fort. The entrance gate of the fort has a shape of quadratic polynomial (parabolic). The mathematical representation of the gate is shown in the figure.

Based on the above information, answer the following questions.

Find the zeroes of the polynomial represented by the graph.
What will be the value of polynomial, represented by the graph, when x = 4?
What will be the expression for the polynomial represented by the graph?
Or
If one zero of a polynomial p(x) is 7 and product of its zeroes is -35, then p(x) = ?

Answer

$1. 1, 3$
$2. -3$
$3. -x^2 + 4x - 3$
$Or$
$-x^2 + 2x + 35$

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Question 24 Marks

Quadratic polynomial can be used to model the shape of many architectural structures in the world. Pershing field of Jersey city in US is one such structure.

Based on the above information, answer the following questions.

If the Arch is represented by $10x^2 - x - 3$, then its zeroes are:
The quadratic polynomial whose sum of zeroes is 0 and product of zeroes is 1 is given by?
Which of the following has $\frac{-1}{2}$ and 2 as their zeroes?
Or
The product of zeroes of the polynomial $\sqrt{3}\text{x}^2-14\text{x}+8\sqrt{3}$ is:

Answer

1. $\frac{-1}{2}, \frac{3}{5}$
2. $x^2 + 1$

3. $2x^2 - 3x - 2$
Or
8

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Question 34 Marks

Pankaj's father gave him some money to buy avocado from the market at the rate of $p(x) = x^2 - 24x + 128$. Let $\alpha,\beta$ are the zeroes of p(x).

Based on the above information, answer the following questions.

Find the value of $\alpha+\beta+\alpha\beta.$
The value of p(2) is?
If $\alpha$ and $\beta$ are zeroes of $x^2 + x - 2,$ then $\frac{1}{\alpha}+\frac{1}{\beta}=$
Or
If sum of zeroes of $q(x) = kx^2 + 2x + 3k$ is equal to their product, then k = ?

Answer

1. 8, 16
2. 84

3. $\frac{1}{2}$
Or
$\frac{-2}{3}$

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Question 44 Marks

ABC construction company got the contract of making speed humps on roads. Speed humps are parabolic in shape and prevents overspeeding, minimise accidents and gives a chance for pedestrians to cross the road. The mathematical representation of a speed hump is shown in the given graph.

Based on the above information, answer the following questions.

The polynomial represented by the graph can be which polynomial?
The zeroes of the polynomial represented by the graph are?
If $\alpha$ and $\beta$ are the zeroes of the polynomial represented by the graph such that $\beta>\alpha,$ then $|8\alpha\ +\ \beta|= $
Or
The expression of the polynomial represented by the graph is?

Answer

1. Quadratic
2. -1, 5

3. 3
Or
$-x^2 + 4x + 5$

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Question 54 Marks

Just before the morning assembly a teacher of kindergarten school observes some clouds in the sky and so she cancels the assembly. She also observes that the clouds has a shape of the polynomial. The mathematical representation of a cloud is shown in the figure.

Find the zeroes of the polynomial represented by the graph.
What will be the expression for the polynomial represented by the graph?
What will be the value of polynomial represented by the graph, when x = 3?
Or
If $\alpha$ and $\beta$ are the zeroes of the polynomial $f(x) = x^2 + 2x - 8$, then $\alpha^4+\beta^4=$

Answer

1. $\frac{1}{2}, \frac{-7}{2}$
2. $p(x) = -4x^2- 12x + 7$

3.-65
Or
272

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MATHS Case study (4 Marks)

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