Find the roots of the equation $\displaystyle x^{2}-x-3=0 $. The nature of the roots is

To determine the nature of the roots, we calculate the discriminant using the formula D = b^2 - 4ac. Substituting a = 1, b = -1 and c = -3 gives D = (-1)^2 - 4(1)(-3), which equals 1 + 12 or 13. Since 13 is not a perfect square and is positive, the roots are real and irrational.

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