复数(2x^2+5x+2)+(x^2+x-2)i为纯虚数则实数x满足

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复数(2x^2+5x+2)+(x^2+x-2)i为纯虚数则实数x满足
复数(2x^2+5x+2)+(x^2+x-2)i为纯虚数则实数x满足

复数(2x^2+5x+2)+(x^2+x-2)i为纯虚数则实数x满足
(1) 2x^2+5x+2=0
(2x+1)(x+2)=0
x1=-1/2,x2=-2
(2) x^2+x-2≠0
(x-1)(x+2)≠0
x≠1,x≠-2
∴x=-1/2

复数(2x^2+5x+2)+(x^2+x-2)i为纯虚数,那么2x^2+5x+2=0且x^2+x-2≠0
可解得x=-1/2(x=-2舍去)