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2 months ago

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What is the positive solution to the equation 0 = –x2 + 2x + 1? Quadratic formula: x = StartFraction negative b plus or minus St

artRoot b squared minus 4 a c EndRoot Over 2 a EndFraction –2 + StartRoot 2 EndRoot 2 – StartRoot 2 EndRoot 1 + StartRoot 2 EndRoot –1 + StartRoot 2 EndRoot

2 answers:

zzz [12.3K]2 months ago

9 0

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.

lawyer [12.5K]2 months ago

3 0

Answer:

C on edge.

Step-by-step explanation:

I just completed the test!

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