Question

Finding the Roots:

The roots of a quadratic equation are the values of x where the equation equals zero. To find the roots, set y to zero and solve for x:
x²−2x−3=0

Answer 1

To find the roots of the quadratic equation x²-2x-3=0, we can use the quadratic formula -x = (-b ± √(b^2-4ac)) / (2a). Plugging in the values of a, b, and c, and simplifying the expression, we find that the roots are x = 3 or x = -1.

Step-by-step explanation:

To find the roots of a quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2-4ac)) / (2a). For the equation x²-2x-3=0, we can identify the values of a, b, and c as follows: a = 1, b = -2, and c = -3. Plugging these values into the quadratic formula, we get: x = (-(-2) ± √((-2)^2 - 4(1)(-3))) / (2(1)). Simplifying this expression, we have: x = (2 ± √(4 + 12)) / 2. Further simplifying, we obtain: x = (2 ± √16) / 2. Continuing, we have: x = (2 ± 4) / 2. Therefore, the roots of the equation are x = 3 or x = -1.