10. A five digit code is used to alarm the safe. The first digit of the code must be an even and the 3rd digit
must be either the number 3 or 5. The numbers do
not repeat. How many different codes could there be?
FCP PERMUATION COMBINATION

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Ответ:

rightdimple3692

10.05.2023

Mathematics

The another root of the polynomial x^2-4x+1=0 is $2-\sqrt{3}$

Step-by-step explanation:

let $x=2+\sqrt{3}$ is a polynomial root.

Subtracting both sides by 2, we get

$x-2=\sqrt{3}$

Squaring both sides, we get

$(x-2)^2=(\sqrt{3})^2$

x^2+4-4x=3

On solving we get,

x^2-4x+1=0

Using quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

If one of the root of the polynomial is $2+\sqrt{3}$ ; then another root by quadratic formula is $2-\sqrt{3}$

or else we can say that irrational roots will always come in conjugate pairs.

Sso, if $2+\sqrt{3}$ is a root, then $2-\sqrt{3}$ is also a root.

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10. A five digit code is used to alarm the safe. The first digit of the code must be an even and the 3rd digit must be either the number 3 or 5. The numbers do not repeat. How many different codes could there be? FCP PERMUATION COMBINATION