Final answer:
The nature of the roots of the given equation y²-5y-3=0 is real and distinct.
Step-by-step explanation:
The given equation is a quadratic equation of the form y²-5y-3=0. To find the nature of the roots, we need to determine the discriminant (D) of the quadratic equation. The discriminant is given by the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 1, b = -5, and c = -3. Substituting these values into the discriminant formula, we get D = (-5)² - 4(1)(-3) = 25 + 12 = 37.
Since the discriminant (D) is positive (D > 0), the quadratic equation has two distinct real roots. Therefore, the nature of the roots of the given equation y²-5y-3=0 is real and distinct.