Question

In the given polynomial, x^2 - 2x - 5^1/2
Find the value of alpha - beta

Answer 1

$\bigstar$ Answer :

Given polynomial is x² - 2x - √5.

Compare this polynomial with ax² + bx + c .

We get ,

• a = 1 , b = -2 , c = -√5

Let α , β be zeroes of the polynomial .

So , sum of zeroes ,

α + β = -b/a = -(-2) / 1 = 2

=> α + β = 2 ... (1)

Product of zeroes ,

α . β = c/a = -√5/1 = -√5

=> α . β = -√5 ... (2)

Now , (a-b)² = (a+b)² - 4ab

$\implies \alpha -\beta =\sqrt{(\alpha+\beta )^2-4\alpha .\beta } \\\\\implies \alpha -\beta = \sqrt{2^2-4(-\sqrt{5} )} \\\\\implies \bold{\bf{\red{\alpha -\beta = 2(\sqrt{1+\sqrt{5}}} }})$