Question

show that root 2 is a zero of the polynomial x square -2 root 2 X + 2​

Answer 1

(x^2)-2=0

x^2=2

x=+√2 or -√2

Answer 2

$\sqrt{2}$ is a zero of the given quadratic polynomial, proved.

Step-by-step explanation:

Let the given quadratic polynomial:

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

Show that, $\sqrt{2}$ is a zero of the given quadratic polynomial = ?

P(x) = $x^{2}-2\sqrt{2}x$ + 2     ....... (1)

Put x = $\sqrt{2}$ in equation (1), we get

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

⇒ P($\sqrt{2}$) = 2 - 2(2) + 2

⇒ P($\sqrt{2}$) = 4 - 4

⇒ P($\sqrt{2}$) = 0

∴ $\sqrt{2}$ is a zero of the given quadratic polynomial, proved.

Thus, $\sqrt{2}$ is a zero of the given quadratic polynomial, proved.