Question

show that root2 is a zero of the polynomila xsquare-2root2x+2​

Answer 1

Answer:

Yes √2 is a zero.

Step-by-step explanation:

If we put the value of x in this polynomial and get 0 as final answer then it is right value for x.

So,

${x}^{2} - 2 \sqrt{2} x + 2 = 0 \\ {( \sqrt{2)} }^{2} - 2 \sqrt{2} \times \sqrt{2} + 2 = 0 \\ 2 - 4 + 2 = 0 \\ 0 = 0$

I hope it will help you.☝

Answer 2

Root 2 is a zero of given polynomial

Solution:

Given that polynomial is:

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

We have to show that $\sqrt{2}$ is a zero of polynomial

Zeroes of Polynomial are the real values of the variable for which the value of the polynomial becomes zero

Let,

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

$If,\ \sqrt{2} \text{ is a zero of f(x) then, } f(\sqrt{2}) = 0$

$Substitute\ x = \sqrt{2}\ in\ f(x)$

$f(\sqrt{2}) = (\sqrt{2})^2 - 2\sqrt{2} \times \sqrt{2} + 2\\\\Simplify\\\\We\ know\ that\ \sqrt{a} \times \sqrt{a} = a\\\\f(\sqrt{2}) = 2 -2(2) + 2\\\\f(\sqrt{2}) = 2 - 4 + 2\\\\f(\sqrt{2}) = 4 - 4\\\\f(\sqrt{2}) = 0$

Thus, $\sqrt{2}$ is zero of given polynomial

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