Difference between revisions of "1962 AHSME Problems/Problem 21"
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==Solution== | ==Solution== | ||
| − | {{ | + | If a quadratic with real coefficients has two non-real roots, the two roots must be complex conjugates of one another. |
| + | This means the other root of the given quadratic is <math>\overline{3+2i}=3-2i</math>. | ||
| + | Now Vieta's formulas say that <math>s/2</math> is equal to the product of the two roots, so | ||
| + | <math>s = 2(3+2i)(3-2i) = \boxed{26 \textbf{ (E)}}</math>. | ||
Revision as of 15:22, 16 April 2014
Problem
It is given that one root of 
, with 
and 
real numbers, is 
. The value of is:
Solution
If a quadratic with real coefficients has two non-real roots, the two roots must be complex conjugates of one another.
This means the other root of the given quadratic is 
.
Now Vieta's formulas say that 
is equal to the product of the two roots, so
.
