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x^2 + (a - 2)x - 2a^2 + 5a - 3 = 0 , |x_1|=2|x_2|

Source: 1999 Estonia National Olympiad Final Round grade 10 p2

March 11, 2020
algebraparametertrinomial

Problem Statement

Find all values of aa such that absolute value of one of the roots of the equation x2+(a−2)x−2a2+5a−3=0x^2 + (a - 2)x - 2a^2 + 5a - 3 = 0 is twice of absolute value of the other root.
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