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-8/3, 4/3 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 -8/3.

Product of two zeros is 4/3.

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, the sum of the roots, α +β = -8/3

So, the quadratic polynomial can be written as x² - (-8/3)x + 4/3.

The polynomial can be rewritten as (1/3)[3x² + 8x + 4].

Let 3x² + 8x + 4 = 0

On factoring the polynomial,

3x² + 6x + 2x + 4 = 0

3x(x + 2) + 2(x + 2) = 0

(3x + 2)(x + 2) = 0

Now, 3x + 2 = 0

3x = -2

x = -2/3

Also, x + 2 = 0

x = -2

Therefore, the zeros of the polynomial are -2/3 and -2.

✦ Try This: Find a quadratic polynomial, the sum and product of whose zeroes are -2 and 3, 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

Summary:

A quadratic polynomial whose sum and product of zeroes are -8/3 and 4/3 is x² + (8/3)x + (4/3). The zeros of the polynomial are -2/3 and -2

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