Question 1029499
That is called the quadratic formula. Here it is:
{{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
Because of the + and - before the square root sign,
you get two x's, you can call them {{{ x[1] }}} and {{{ x[2] }}}
They are the roots of the quadratic
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You get the a, b, and c from the general form of the quadratic:
{{{ a*x^2 + b*x + c = 0 }}}
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Here's an example, and it's plot:
{{{ f(x) = x^2 + x + 1/4 }}}
Set {{{ f(x) = 0 }}} to get roots:
{{{ x^2 + x + 1/4 = 0 }}}
{{{ a = 1 }}}
{{{ b = 1 }}}
{{{ c = 1/4 }}}
Plot:
{{{ graph( 400, 400, -4, 4, -10, 10, x^2 + x + 1/4 ) }}}
Note that there is just 1 root ( where the curve touches the x-axis )
This is because {{{ b^2 = 4*a*c }}}