Find the zeroes of the polynomial x² - 3 and verify the relationship between the zeroes and the coefficients

Solution:

We will use the algebraic identity to find the zeroes of the quadratic equation.

a² - b² = (a + b)(a - b)

x² - 3 can be written as (x + √3) (x - √3)

Put both the factors equal to zero.

x + √3 = 0 and x - √3 = 0

x = - √3 and x = √3

The value of the polynomial will be zero when x = - √3 and x = √3.

Thus x = - √3 and x = √3 are the zeroes of the polynomial.

In a quadratic polynomial of the form ax² + bx + c = 0 where a ≠ 0. 

The sum of the zeroes is expressed as - b/ a that is coefficient of x / coefficient of x²

- √3 + √3 = 0 = 0/ 1 (∵ coefficient of x / coefficient of x² )

The product of the zeroes is expressed as c/ a that is constant term/ coefficient of x²

- √3 × √3 = - 1 = - 3/ 1 (∵ constant term/ coefficient of x²)

☛ Check: NCERT Solutions for Class 10 Maths Chapter 2

Find the zeroes of the polynomial x² - 3 and verify the relationship between the zeroes and the coefficients

Summary:

The zeroes of the polynomial x² - 3 are - √3 and √3. The coefficients of the polynomial can be expressed as the sum and the product of the zeroes

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