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21/8, 5/16 find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation

Solution:

Given, the sum of two zeros is 21/8.

Product of two zeros is 5/16.

We have to find the quadratic polynomial and its zeros.

A quadratic polynomial in terms of the zeroes (α,β) is given by

x² - (sum of the zeroes) x + (product of the zeroes)

i.e, f(x) = x² -(α +β) x +αβ

Here, sum of the roots, α +β = 21/8

Product of the roots, αβ = 5/16

So, the quadratic polynomial can be written as x² - 21/8 + 5/16.

The polynomial can be rewritten as (1/16)[16x² - 42x + 5].

Let 16x² - 42x + 5 = 0

On factoring the polynomial,

16x² - 2x - 40x + 5 = 0

2x(8x - 1) - 5(8x - 1) = 0

(2x - 5)(8x - 1) = 0

Now, 2x - 5 = 0

2x = 5

x = 5/2

Also, 8x - 1 = 0

8x = 1

x = 1/8

Therefore, the zeros of the polynomial are 5/2 and 1/8.

✦ Try This: Find a quadratic polynomial, the sum and product of whose zeroes are 2/7 and 3/2, respectively. Also find its zeroes

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.4 Problem 1 (ii)

Summary:

A quadratic polynomial whose sum and product of zeroes are 21/8 and 5/16 is x² - (21/8)x + (5/16). The zeros of the polynomial are 5/2 and ⅛

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