Question 173794
{{{4x^2 - x + 36 = 0}}}
Use quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 4}}}
{{{b = -1}}}
{{{c = 36}}}
{{{x = (-(-1) +- sqrt( (-1)^2-4*4*36 ))/(2*4)}}}
{{{x = ( 1 +- sqrt( 1 - 576 )) / 8 }}}
{{{x = ( 1 +- 5*sqrt( -23 )) / 8 }}}
{{{x = ( 1 +- 5*sqrt(23)*i) / 8 }}}
{{{a^2 = (1 + 5*sqrt(23)*i)/8}}}
{{{b^2 = (1 - 5*sqrt(23)*i)/8}}}
{{{1/a^2 = 8/(1 + 5*sqrt(23)*i)}}}
{{{1/b^2 = 8/(1 - 5*sqrt(23)*i)}}}
If roots are {{{r[1]}}} and {{{r[2]}}},
{{{(x - r[1])(x - r[2]) = x^2 - (r[1] + r[2])x +  r[1]r[2]}}}
{{{r[1] + r[2] = 8/(1 + 5*sqrt(23)*i) + 8/(1 - 5*sqrt(23)*i)}}}
{{{r[1] + r[2] = 8*(1 - 5*sqrt(23)*i + 1 + 5*sqrt(23)*i)}}}
{{{r[1] + r[2] = 16}}}
{{{r[1]r[2] = 8/(1 + 5*sqrt(23)*i) * 8/(1 - 5*sqrt(23)*i)}}}
{{{r[1]r[2] = 64 / (1 - 25*23*(-1))}}}
{{{r[1]r[2] = 64 / 576}}}
{{{r[1]r[2] = 1/9}}}
The equation is
{{{(x - r[1])(x - r[2]) = x^2 - (r[1] + r[2])x +  r[1]r[2]}}}
{{{(x - r[1])(x - r[2]) = x^2 - 16x +  (1/9)}}}
{{{x^2 - 16x + (1/9) = 0}}}
{{{9x^2 - 144x + 1 = 0}}} answer
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I'm not sure what the next part is looking for