MathematicsMedium129×since 2002Q5158Let α\alphaα, β\betaβ be the roots of the equation x2−2x+6=0x^{2}-\sqrt{2} x+\sqrt{6}=0x2−2x+6=0 and 1α2+1,1β2+1\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1α21+1,β21+1 be the roots of the equation x2+ax+b=0x^{2}+a x+b=0x2+ax+b=0. Then the roots of the equation x2−(a+b−2)x+(a+b+2)=0x^{2}-(a+b-2) x+(a+b+2)=0x2−(a+b−2)x+(a+b+2)=0 are :Anon-real complex numbersBreal and both negativeCreal and both positiveDreal and exactly one of them is positiveCheck answerSkip