Question 1156958
<br>
If the coefficients of the quadratic {{{x^2+ax+b}}} are real and one root is {{{5-4i}}}, then the other root is {{{5+4i}}}.<br>
Vieta's Theorem says the sum of the roots is -a and the product is b.<br>
The sum of the roots is 10; so -a=10 which means a = -10.<br>
The product of the roots is {{{25-16i^2 = 25+16 = 41}}}; so b = 41.<br>
ANSWER: {{{x^2-10x+41}}}<br>