Question

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Answer 1

Step-by-step explanation:

Let the zeroes of quadratic polynomial be alpha and beta.

alpha + beta= root3

alpha × beta=1/root3

Quadratic polynomial is

x^2-root3x+1/root3

Answer 2

Answer:

$\large\boxed{\sf{\sqrt{3}{x}^{2}-3x+1}}$

Step-by-step explanation:

Given, for a quadratic polynomial,

Sum of zeroes = √3

Product of zeroes = 1/√3

To find the quadratic polynomial.

We know that,

A quadratic polynomial is given by,

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

Substituting the values, we will get,

$= {x}^{2} - \sqrt{3} x + \dfrac{1}{ \sqrt{3} }$

Multiplying with √3 , we get,

$= \sqrt{3} {x}^{2} - 3x + 1$

Hence, the required quadratic polynomial is $\sqrt{3}{x}^{2}-3x+1$