- #1
diredragon
- 323
- 15
Homework Statement
if x1 and x2 are solutions to 1) x² + x + 1 = 0, then 2) y1 = ax1 + x2 and 3) y2 = x1 + ax2 are solutions to which quadratic equation?
Homework Equations
ax² + bx + c = 0
x1∕2 = (−b ± √(b² - 4ac))/2a
The Attempt at a Solution
Well, firstly i solved for x1 and x2 getting:
x1 = (−1 + √(-3))/2
x2 = (−1 - √(-3))/2
I now have in mind to replace the x1 and x2 in equations 2) and 3), and after i simplify best i can to find the equation by means of following formula:
(y - y1)(y - y2)
Will this yield the solution, and is there a simpler way of doing this? The simplification alone is a hard task letalone the multiplication that comes afterwards.
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