=> (0)2 x2+(0)bx=b2
x2+bx =b2
x2=b3

IT WAS NOT CONFIRMED ANSWER.
BUT I WILL TRY.

Roots of the quadratic equation:

The quadratic equation given is a^2x^2 + abx - b^2 = 0.

To find the roots of this equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = a^2, b = ab, and c = -b^2.

Now let's substitute these values into the quadratic formula and simplify:

x = (-ab ± √((ab)^2 - 4(a^2)(-b^2))) / 2(a^2)

x = (-ab ± √(a^2b^2 + 4a^2b^2)) / 2(a^2)

x = (-ab ± √(5a^2b^2)) / 2(a^2)

x = (-ab ± ab√5) / 2(a^2)

Simplifying further, we can cancel out the common factor of ab:

x = (-1 ± √5) / 2a

From this equation, we can see that the roots of the quadratic equation are unequal.

Explanation:

The options provided are:
a) Equal
b) Non-real
c) Unequal
d) None of these

The correct answer is option 'c', which states that the roots are unequal. We can see this from the quadratic formula derived above. The roots of the equation are given by (-1 ± √5) / 2a. Since the value inside the square root (√5) is not zero, the roots will be distinct and therefore unequal.

If the roots were equal, the value inside the square root (√5) would have been zero, resulting in a single root.

If the roots were non-real, the value inside the square root (√5) would have been negative, resulting in imaginary roots. However, in this case, the value inside the square root is positive (√5), indicating that the roots are real.

Hence, the correct answer is option 'c', which states that the roots are unequal.