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-2√3, -9 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 -2√3.

Product of two zeros is -9.

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 = -2√3

Product of the roots, αβ = -9

So, the quadratic polynomial can be written as x² - (-2√3)x + (-9)

= x² + 2√3x - 9.

Let x² + 2√3x - 9 = 0

On factoring the polynomial,

x² + 3√3x - √3x - 9 = 0

x(x + 3√3) - √3(x + 3√3) = 0

(x - √3)(x + 3√3) = 0

Now, x - √3 = 0

x = √3

Also, x + 3√3 = 0

x = -3√3

Therefore, the zeros of the polynomial are -3√3 and √3.

✦ Try This: Find a quadratic polynomial, the sum and product of whose zeroes are -2/3 and √5, 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 (iii)

Summary:

A quadratic polynomial whose sum and product of zeroes are -2√3 and -9 is x² + 2√3x - 9. The zeros of the polynomial are √3 and -3√3

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