Question 175025
{{{ 2x^2 - 12x + k = 0}}}
{{{x^2 - 6x + k/2 = 0}}}
given:
{{{r[1] = 3 + sqrt(2)}}}
{{{(x - r[1])(x - r[2]) = 0}}}
{{{x^2 - (r[1] + r[2])*x + r[1]r[2] = 0}}}
{{{-6 = -(3 + sqrt(2) + r[2])}}}
{{{r[2] = 3 - sqrt(2)}}} the missing root
------------------------
{{{k/2 = r[1]r[2]}}}
{{{k = 2*(3 + sqrt(2))*r[2]}}}
{{{k = 2*(3 + sqrt(2))(3 - sqrt(2))}}}
{{{k = 2*(9 - 2)}}}
{{{k = 14}}}
The equation is
{{{ 2x^2 - 12x + 14 = 0}}}
check:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 2}}}
{{{b = -12}}}
{{{c = 14}}}
{{{x = (-(-12) +- sqrt( (-12)^2-4*2*14 ))/(2*2) }}}
{{{x = ( 12 +- sqrt( 144 - 112 ))/4 }}}
{{{x = ( 12 +- sqrt( 32 ))/4 }}}
{{{x = (3 + sqrt(2))}}}
{{{x = (3 - sqrt(2))}}}
OK