Question

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

Answer 1

Answer:

$1+\sqrt{2}$

Step-by-step explanation:

If a quadratic equation is defined as

$ax^2+bx+c=0$          .... (1)

then the quadratic formula is

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

The given quadratic equation is

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

It can we written as

$-x^2+2x+1=0$             .... (2)

On comparing (1) and (2) we get

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

Substitute these values in the quadratic formula.

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

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

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

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

Taking out common factors.

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

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

Two roots are

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

We know that

$\sqrt{2}=1.41$

So

$1$

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

Answer 2

Answer:

C on edge

Step-by-step explanation:

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