Let α, β be the roots of the equation x²-√(2) x+√(6)=0 and 1/(α²)+1, 1/(β²)+1 be the roots of the equation x²+a x+b=0. Then the roots of the equation x²-(a+b-2) x+(a+b+2)=0 are:

(D) real and exactly one of them is positive

Complex Numbers and Quadratic Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jul, Evening shift · Q5158

JEE Main 202228 Jul, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha

\beta

be the roots of the equation

x^{2}-\sqrt{2} x+\sqrt{6}=0

and

\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1

be the roots of the equation

x^{2}+a x+b=0

. Then the roots of the equation

x^{2}-(a+b-2) x+(a+b+2)=0

are :

JEE Main 2022 · 28 Jul, Evening shift · Q5158

JEE Main 202228 Jul, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha

\beta

be the roots of the equation

x^{2}-\sqrt{2} x+\sqrt{6}=0

and

\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1

be the roots of the equation

x^{2}+a x+b=0

. Then the roots of the equation

x^{2}-(a+b-2) x+(a+b+2)=0

are :