# Enhanced Curriculum Support

**Sample question paper**

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### SectionA

**1. The sum of the zeroes of the polynomial 2**

**2. The degree of the polynomial 4**

**3. If one root of the quadratic polynomial **

**Answers**

2

3

-10

### SectionB

**1. Determine the polynomial whose zeroes are α and β given α+β = 3 and αβ=2**

**2.Find the zeroes of the polynomial **

**3. What is the remainder when **

**Answers**

The polynomial is

-3x+2x 2 The zeroes are 2 and 3.

The remainder is -6.

### SectionC

**1.Find the zeroes of the polynomial 2**

**2.If the polynomial **

**Answers**

The zeroes are 1 and 3.

The quotient is

-4x+3.x 2

### SectionD

**1.Find a quadratic polynomial whose zeroes are 5 and -3. Also, verify the relationship between the zeroes and the coefficients.**

**Answers**

- The polynomial is
-2x-15x 2

**Value based questions**

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### problem1

**Situation:**

**A small business owner is trying to calculate his profit over several months. The profit (in thousands) in the first month was p. Each month, the profit increased by a constant amount d.**

**1.If the profit after n months is represented by a polynomial P(x)= p + d(n-1),calculate the profit after 6 months if the initial profit was $2000, and the monthly increase in profit was $500**

**Answer**

P(6)= 2000+ 500(6-1) = 2000 + 500 x 5 = 2000 + 2500 = 4500

So, the profit after 6 months is $4500

### problem2

**Situation:**

**A farmer wants to divide his rectangular land into smaller plots. The length of the land is l meters, and the width is w meters. He wants to divide the length and width into smaller plots each increasing by x meters.**

**1.If the area of the land is given by the polynomial A(x)= l x w + x(l+w)+ **

**Answer**

A(5)= 50 x 30 + 5(50+30) +

**So, the area of the land after the division is 1925 square meters.**

### problem3

**Situation:**

**The population of a town is modeled by a polynomial function P(t)=**

**Find the population after 3 years.**

**Answer**

P(3) =

**Hots**

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### question1

**1.Find the Quadratic Polynomial whose sum and product of zeroes are √2+1, .**

**Answers:**

- sum = 2√2, product = 1

Quadratic Polynomial =

### question2

**1. On dividing the polynomial 4**

**Answers:**

- g(x)=4
+7x+2x 2

### question3

**1.If the squared difference of the zeroes of the quadratic polynomial **

**Answers:**

- p+- 18

**Ncert exemplar solutions**

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**Answer Ncert exemplar questions**

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### questions

A quadratic polynomial, whose zeroes are –3 and 4, is

Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -

respectively. Also find its zeroes.3 2 If the remainder on division of

+x 3 2 + kx +3 by x – 3 is 21, find the quotient and the value of k. Hence, find the zeroes of the cubic polynomialx 2 +x 3 2 + kx-18.x 2 Find the zeroes of the polynomial

+x 2 x -2, and verify the relation between the coefficients and the zeroes of the polynomial.1 6 Can x – 1 be the remainder on division of a polynomial p (x) by 2x + 3? Justify your answer.

Is the following statement True or False? Justify your answer. If the zeroes of a quadratic polynomial

+bx+c are both negative, then a, b and c all have the same sign.ax 2

### Ans

**Answers**

-x 2 2 -6x 2 the zeroes are - and

+x 3 2 + kx-18 are 3, – 2, – 3.x 2 Hence,

and4 3 − are the zeroes of the given polynomial.3 2 No, since degree (x – 1) = 1 = degree (2x + 3).

True, because

− = sum of the zeroes < 0, so thatb a >0.Also the product of the zeroes=b a >0.c a

**Case-Based Questions**

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### question

The natural shape of a banana can show the curve of a quadratic polynomial, which is in the form of

p(x) =

**Based on your understanding of the above case study,answer all the five questions below:**

**(1)The number of zeroes in the polynomial for the shape of the banana is**

**(2)If the curve of the banana is represented by the polynomial then the zeroes are**

**(3)If the representation of curve of banana whose one zero is 4 and the sum of the zeroes is 0, the quadratic polynomial is**

**(4)Each zero of the polynomial is decreased by 2. The resulting polynomial is P(x)= **

**(5)If the curve representing the polynomial P(x)=(**

**Answers**

1

0

-16x 2 b =3 and c=5

mp=nq