11 days ago

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros for

3, 5+ square root of 5

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zzz [12365]

Answer:

$1+\sqrt{2}$

Step-by-step explanation:

Consider a quadratic equation given by

$ax^2+bx+c=0$ .... (1)

The quadratic formula then is

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

The quadratic equation provided is

$0=-x^2+2x+1$

This can be expressed as

$-x^2+2x+1=0$ .... (2)

By comparing (1) and (2), we derive:

$a=-1,b=2,c=1$

Plug these values into the quadratic formula.

$x=\dfrac{-2\pm \sqrt{2^2-4(-1)(1)}}{2(-1)}$

$x=\dfrac{-2\pm \sqrt{4+4}}{-2}$

$x=\dfrac{-2\pm \sqrt{8}}{-2}$

$x=\dfrac{-2\pm 2\sqrt{2}}{-2}$

Factoring out common elements.

$x=\dfrac{-2(1\pm \sqrt{2})}{-2}$

$x=1\pm \sqrt{2}$

The two solutions are

$x=1+\sqrt{2}$ and $x=1-\sqrt{2}$

We recognize that

$\sqrt{2}=1.41$

Thus,

$1$

Consequently, root $x=1+\sqrt{2}$ is positive while $x=1-\sqrt{2}$ is negative.

9 0

2 months ago

lawyer [12517]

Answer:

in steps

Step-by-step explanation:

In a fair roulette game, the likelihood of the ball landing on RED remains constant, regardless of prior spins.

a) 18/38

b) 18/38

c) Yes, I have confidence in my responses. Since it's fair, the number of RED slots does not change.

8 0

1 month ago