NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 2 Polynomials Class 10 NCERT Solutions Ex 2.2. 

• Polynomials Class 10 Ex 2.1
• Polynomials Class 10 Ex 2.3
• Polynomials Class 10 Ex 2.4

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

Page No: 33

Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x² – 2x – 8

(ii) 4s² – 4s + 1

(iii) 6x² – 3 – 7x

(iv) 4u² + 8u

(v) t² – 15

(vi) 3x² – x – 4

Solution:

So, the zeroes of x² – 2x – 8 are 4 and -2.

Concept Insight: The zero of a polynomial is that value of the variable which when substituted in the polynomial makes its value 0. When a quadratic polynomial is equated to 0, then the values of the variable obtained are the zeroes of that polynomial. The relationship between the zeroes of a quadratic polynomial with its coefficients is very important. Also, while verifying the above relationships, be careful about the signs of the coefficients.

Question 2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i) 1/4, -1

(ii) √2, 1/3

(iii) 0, √5

(iv) 1,1

(v) -1/4,1/4

(vi) 4,1

Solution:

(i)    Let the required polynomial be  ax² + bx + c, and let its zeroes α and β

If a = 4k, then b = -k, c = -4k  Therefore, the quadratic polynomial is k(4 x ² – x – 4), where k is a real number .

(ii)     Let the polynomial be  ax² + bx + c, and let its zeroes be α and β



(iii)    Let the polynomial be  ax² + bx + c, and let its zeroes be α and β





(iv)    Let the polynomial be  ax² + bx + c, and let its zeroes be α and β

Therefore, the quadratic polynomial is k(x² – x + 1), where k is a real number.



(v)    Let the polynomial be ax² + bx + c, and its zeroes be α and β

Therefore, the quadratic polynomial is k(4x² + x + 1),where k is a real number .

(vi)    Let the polynomial be ax² + bx + c.



Therefore, the quadratic polynomial is k(x² – 4x + 1), where k is a real number.

Concept Insight:  Since the sum and product of zeroes give 2 relations between three unknowns so we assign a value to the variable a and obtain other values.

Alternatively, If the sum and the product of the zeroes of a quadratic polynomial is given then polynomial is given by, where k is a constant. And the simplest polynomial will be the one in which k = 1.

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