Question

Show that √2 is a zero of the polynomial x square-2√2x+2

Answer 1

Proof:

Method 1.

The given polynomial is

f(x) = x² - 2√2 x + 2

= x² - √2 x - √2 x + 2

= x (x - √2) - √2 (x - √2)

= (x - √2) (x - √2)

Thus √2 is a zero of the given polynomial.

Method 2.

The given polynomial is

f(x) = x² - 2√2 x + 2

Now f(√2) = (√2)² - 2√2 (√2) + 2

= 2 - 4 + 2

= 0

∵ x = √2 satisfies f(x) = 0, √2 is a zero of f(x).

Thus proved.