(A) The given quadratic equation is $2ax^2 + (2a + b)x + b = 0$. The discriminant $D$ is given by $D = B^2 - 4AC$. Here,$A = 2a$,$B = (2a + b)$,and $C

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(A) The given quadratic equation is $2ax^2 + (2a + b)x + b = 0$. The discriminant $D$ is given by $D = B^2 - 4AC$. Here,$A = 2a$,$B = (2a + b)$,and $C = b$. $D = (2a + b)^2 - 4(2a)(b) = 4a^2 + 4ab + b^2 - 8ab = 4a^2 - 4ab + b^2 = (2a - b)^2$. Since $a$ and $b$ are integers,$(2a - b)^2$ is a perfect square. If the discriminant of a quadratic equation with rational coefficients is a perfect square,the roots are rational. Thus,the roots are rational.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If $a$ and $b$ are odd integers,then the roots of the equation $2ax^2 + (2a + b)x + b = 0$,where $a \neq 0$,are

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rational
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irrational
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non-real
D
equal

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