How to find the roots of a quadratic polynomial?

To find the roots of a quadratic polynomial, use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.

A quadratic polynomial is a polynomial of degree 2, meaning it has a highest power of x of 2. It can be written in the form ax² + bx + c, where a, b, and c are constants. To find the roots of this polynomial, we need to solve for x when the polynomial equals 0.

The quadratic formula is a formula that gives us the roots of any quadratic polynomial. It is derived from completing the square on the quadratic equation ax² + bx + c = 0. The formula is x = (-b ± √(b² - 4ac)) / 2a.

To use the quadratic formula, we simply plug in the values of a, b, and c from our quadratic polynomial. Then we simplify the expression under the square root, and solve for x using the plus/minus sign. If the expression under the square root is negative, then the roots are imaginary and the polynomial does not intersect the x-axis.

For example, let's find the roots of the quadratic polynomial 2x² + 5x - 3. Using the quadratic formula, we have x = (-5 ± √(5² - 4(2)(-3))) / 2(2). Simplifying, we get x = (-5 ± √49) / 4. So the roots are x = (-5 + 7) / 4 and x = (-5 - 7) / 4, which simplify to x = 1/2 and x = -3.