Nature of roots of quadratic equation

• Quadratic equations' roots are the values of the variables that satisfy the equation. They're also known as the quadratic equation's “solutions” or “zeros.” Because they satisfy the equation, the roots of the quadratic equation x² – 7x + 10 = 0 are x = 2 and x = 5. i.e., when x = 2, 22 – 7(2) + 10 = 4 – 14 + 10 = 0.
• The discriminant is calculated by taking the square root of b² - 4ac
• If the discriminant is positive, there will be two real solutions to the quadratic formula.
• If the discriminant is zero, then the quadratic has one real solution which is called a repeated root.
• If the discriminant is negative, then there will be no real solutions but instead complex conjugate pairs of imaginary numbers.
• Complex numbers have an imaginary part represented by j.
• A quadratic function can only have at most two zeros/roots.
• When we graph a quadratic function, it forms a parabola with its vertex located on the line y=f(a). The axis of symmetry passes through this point.
• A complex number can be written in standard form as a+bi where a and b are real numbers and i represents the imaginary unit.
• To find the roots of a quadratic equation with complex coefficients, we use the quadratic formula with the complex coefficient substituted into it.
• To find the x-intercepts of a parabola, set y = 0 and solve for x using the quadratic formula.
• The x-coordinate of the vertex is -b/(2a)
• The y-coordinate of the vertex is f(-b/(2a))