![]() Relationship Between Coefficients and Roots of Quadratic Equation D Based on the discriminant value the nature of the roots of the quadratic equation can be predicted. The value b 2 - 4ac is called the discriminant of a quadratic equation and is designated as 'D'. This is possible by taking the discriminant value, which is part of the formula to solve the quadratic equation. The nature of roots of a quadratic equation can be found without actually finding the roots (α, β) of the equation. Nature of Roots of the Quadratic Equation And also check out the formulas to find the sum and the product of the roots of the equation. Here we shall learn more about how to find the nature of roots of a quadratic equation without actually finding the roots of the equation. These roots of the quadratic equation are also called the zeros of the equation. The roots of a quadratic equation are referred to by the symbols alpha (α), and beta (β). The roots of a quadratic equation are the two values of x, which are obtained by solving the quadratic equation. Thus, by completing the squares, we were able to isolate x and obtain the two roots of the equation. This is good for us, because now we can take square roots to obtain: The left hand side is now a perfect square: Now, we express the left hand side as a perfect square, by introducing a new term (b/2a) 2 on both sides: To determine the roots of this equation, we proceed as follows: For a For negative value of a (a 0, the range of the quadratic equation ax 2 + bx + c = 0 is [b 2 - 4ac/4a, ∞).For D 0), the quadratic expression f(x) = ax 2 + bx + c has a minimum value at x = -b/2a.For D = 0 the roots are real and equal.For D > 0 the roots are real and distinct.The discriminant of the quadratic equation is D = b 2 - 4ac. ![]() The quadratic equation in its standard form is ax 2 + bx + c = 0.The following list of important formulas is helpful to solve quadratic equations. Maximum and Minimum Value of Quadratic Expression Important Formulas for Solving Quadratic Equations We shall learn more about the roots of a quadratic equation in the below content. These two answers for x are also called the roots of the quadratic equations and are designated as (α, β). The quadratic equations are second-degree equations in x that have maximum two answers for x. Did you know that when a rocket is launched, its path is described by a quadratic equation? Further, a quadratic equation has numerous applications in physics, engineering, astronomy,etc. In other words, a quadratic equation is an “ equation of degree 2.” There are many scenarios where a quadratic equation is used. The word " Quadratic" is derived from the word " Quad" which means square. Quadratic equations are second-degree algebraic expressions and are of the form ax 2 + bx + c = 0.
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