What is the nature of the roots of the equati | vedclass

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(A) The given quadratic equation is $a^2x^2 + (a + b)x - b^2 = 0$.Comparing this with $Ax^2 + Bx + C = 0$,we have $A = a^2$,$B = (a + b)$,and $C = -b^

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Real and distinct

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(A) The given quadratic equation is $a^2x^2 + (a + b)x - b^2 = 0$.Comparing this with $Ax^2 + Bx + C = 0$,we have $A = a^2$,$B = (a + b)$,and $C = -b^2$.The discriminant $D$ is given by $D = B^2 - 4AC$.$D = (a + b)^2 - 4(a^2)(-b^2) = (a + b)^2 + 4a^2b^2$.Since $(a + b)^2 \ge 0$ and $4a^2b^2 \ge 0$,the sum $D = (a + b)^2 + 4a^2b^2$ must be greater than $0$ (assuming $a, b 
eq 0$).Since $D > 0$,the roots are real and distinct.

What is the nature of the roots of the equation $a^2x^2 + (a + b)x - b^2 = 0$?

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