If $a,b \in R$ then the equation $x^2-abx-a^2=0$ has

To determine the nature of the roots of x^2 - abx - a^2 = 0, we evaluate the sum and the product of the roots. The product of the roots is given by c/a, which is -a^2; since a is a real number, a^2 is always non-negative, making -a^2 zero or negative. A negative product indicates that the roots must have opposite signs, meaning the equation has one positive and one negative root. The sum of the roots is ab, which does not change this conclusion about the signs.

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