The roots of the equation $x^ {2}+ax-4=0$ are, where $a\in R$

To determine the nature of the roots for the quadratic equation x^2 + ax - 4 = 0, we evaluate the discriminant using the formula D = b^2 - 4ac. Substituting the coefficients gives D = a^2 - 4(1)(-4), which simplifies to a^2 + 16. Since the square of any real number is non-negative, a^2 is always zero or positive, making the discriminant a^2 + 16 strictly greater than zero for all real values of a. A positive discriminant means the equation always has two real and distinct roots.

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