Question

X2-2√5x+3
Split the middle term

Answer 1

x² - 2√5x + 3
= x² -{(√5 +√2) + (√5 - √2)}x + (√5 - √2)(√5 + √2)
= x² - (√5 + √2)x - (√5 -√2)x + (√5 + √2)(√5 - √2)
= x[x - √5 - √2] - (√5 - √2)[x - √5 - √2]
= [x - √5 - √2][x - √5 + √2]

Hence, x = √5 ± √2 are the zeros of given expression

Answer 2

[math]\cfrac{-(-2\sqrt{5})\pm\sqrt{(-2\sqrt{5})^2 - 4\times1\times3}}{2\times1} = \sqrt{5}\pm\sqrt{2}[/math]

[math]\implies x^2 - 2\sqrt{5}x + 3 = [x - (\sqrt{5} + \sqrt{2})][x - (\sqrt{5} - \sqrt{2})][/math]