Question 766506
Q:
Derive a quadratic equation using: x= {{{(-6 +- 5sqrt(2))/3}}}.
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A:
The sum of the roots is {{{(-6 + 5sqrt(2))/3}}} + {{{(-6 - 5sqrt(2))/3}}} = -4.
The product of the roots is {{{((-6 + 5sqrt(2))/3)((-6 - 5sqrt(2))/3)}}} = {{{(36 - 50)/9}}} = {{{-14/9}}}.
The quadratic equation is {{{x^2}}} - (sum of roots){{{x}}} + (product of roots) = 0.
{{{x^2 + 4x - 14/9 = 0}}}, multiply both sides by 9.
ANSWER: {{{highlight(9x^2 + 36x - 14 = 0)}}}