Quadratic Equations PDF

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Quadratic Equations

A quadratic equation in the variable x is of the form ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α, β).

A quadratic polynomial, when equated to zero, becomes a quadratic equation. The values of x satisfying the equation are called the roots of the quadratic equation.

Quadratic Equation Formula

The solution or roots of a quadratic equation are given by the quadratic formula:
(α, β) = [-b ± √(b2 – 4ac)]/2a

Roots of Quadratic Equation

The values of variables satisfying the given quadratic equation are called its roots. In other words, x = α is a root of the quadratic equation f(x), if f(α) = 0.

The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersect the x-axis.

  • One of the roots of the quadratic equation is zero and the other is -b/a if c = 0
  • Both the roots are zero if b = c = 0
  • The roots are reciprocal to each other if a = c

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Quadratic Equations

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