Question

Show that root 2 is a zero of the polynomial x2-2√2x+2

Answer 1

Step-by-step explanation:

so root 2is zero of the polynomial x

$x ^{2} - 2 \sqrt{2x } + 2$

Answer 2

√2 is the zero of the polynomial $x^{2} - 2\sqrt{2}x + 2$ .

• If √2 is the zero of the polynomial then the value of the polynomial will be equal to zero when the zero is substituted in the polynomial.
• Substituting √2 in the polynomial and evaluating the value of the polynomial , we get

$x^{2} - 2\sqrt{2}x + 2$

= ${(\sqrt{2})}^{2} - 2\sqrt{2}(\sqrt{2}) + 2$

= $2 - 4 + 2$

= 0

• The value of the polynomial at  is zero. Therefore, √2 is the zero of the polynomial.