Question

What is the positive solution to the equation 0 = –x2 + 2x + 1? Quadratic formula: x = –2 + 2 – 1 + –1 +

Answer 1

The standard form of a quadratic equation is :

ax² + bx + c = 0

And the quadratic formula is:

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

So, first step is to compare the given equation with the above equation to get the value of a, b and c.

So, a = -1, b = 2 and c = 1.

Next step is to plug in these values in the above formula. Therefore,

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

$=\frac{-2\pm\sqrt{4+4}}{-2}$

$=\frac{-2\pm\sqrt{8}}{-2}$

$=\frac{-2\pm\sqrt{4*2}}{-2}$

$=\frac{-2\pm\sqrt{4}*\sqrt{2}}{-2}$

$=\frac{-2\pm2*\sqrt{2}}{-2}$

$=-\frac{-2}{-2} \pm\frac{2\sqrt{2}}{-2}$

So, x =$1 \pm\sqrt{2} .$