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Quadratic Equations. - Coggle Diagram
Quadratic Equations.
FORMATION OF QUADRATIC EQUATION WITH GIVEN ROOTS
1- If α and β are the two roots of a quadratic equation, then the formula to construct the quadratic equation is.
2- x2 - (α + β)x + αβ = 0.
3- x2 - (sum of roots)x + product of roots = 0.
General Form
An equation containing a second-degree polynomial is called a quadratic equation.
Completing Square
Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial . To solve ax2+bx+c=0 by completing the square: 1. Transform the equation so that the constant term, c , is alone on the right side.
Quadratic Formula
What is Delta and Discriminant
İf there are two distinct real roots : Delta > 0
İf there are two equal real roots : Delta = 0
İf there is no real root : Delta < 0
The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a)
Factorisation
Factoring quadratics is a method of expressing the quadratic equation ax2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax2 + bx + c = 0.
Relation between the roots and the coefficients
The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient.
The product of the roots of a quadratic equation is equal to the constant term (the third term),
divided by the leading coefficient.
