# 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:**

The sum of roots and the product of roots are given. We have to form a quadratic polynomial.

Put the values in the general equation of the quadratic polynomial , that is k [x^{2} - (sum of roots) x + (product of roots)] where k is any real number.

Let's assume k = 1 in each case.

(i) 1/4, - 1

We know that the general equation of a quadratic polynomial is:

x^{2} - (sum of roots) x + (product of roots)

x^{2} - (1/4)x + (- 1)

x^{2} - (1/4)x - 1

(ii) √2, 1/3

We know that the general equation of a quadratic polynomial is:

x^{2} - (sum of roots) x + (product of roots)

x^{2} - √2 x + 1/3

(iii) 0, √5

We know that the general equation of a quadratic polynomial is:

x^{2} - (sum of roots) x + (product of roots)

x^{2} - 0 x + √5

x^{2} + √5

(iv) 1, 1

We know that the general equation of a quadratic polynomial is:

x^{2} - (sum of roots) x + (product of roots)

x^{2} - 1x + 1

x^{2} - x + 1

(v) - 1/4, 1/4

We know that the general equation of a quadratic polynomial is:

x^{2} - (sum of roots) x + (product of roots)

x^{2} - (- 1/4)x + 1/4

x^{2} + (1/4)x + 1/4

(vi) 4, 1

We know that the general equation of a quadratic polynomial is:

x^{2} - (sum of roots) x + (product of roots)

x^{2} - 4x + 1

**Video Solution:**

## 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

### NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.2 Question 2 - Chapter 2 Exercise 2.2 Question 2:

**Summary:**

The quadratic polynomials for the given numbers as the sum and product of the polynomials are i) x^{2} - (1/4)x - 1, ii) x^{2} - √2 x + 1/3, iii) x^{2} + √5, iv) x^{2} - x + 1, v) x^{2} + (1/4)x + 1/4 and vi) x^{2} - 4x + 1 respectively.