Question

show that √2 is zero of the polynomial x²-2√2x+2​

Answer 1

Substitute $x=\sqrt{2}$.

x²-2√2x+2​=0

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

$=2-2\sqrt{4} +2$

$=2-4+2$

$=0$ (TRUE)

∴$x=\sqrt{2}$ is a zero of the given polynomial.