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The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
May 28, 2024 · Roots of Quadratic Equations are also called Zeros of a Quadratic Equation or Solutions of a Quadratic Equation. Quadratic equations are mathematical expressions of the form ax 2 + bx + c = 0, where a, b, and c are constants, and x represents the variable.
We shall learn how to find the roots of quadratic equations algebraically and using the quadratic formula. The general form of a quadratic equation is ax 2 + bx + c = 0, where x is the unknown and a, b and c are known quantities such that a ≠ 0.
Jun 6, 2024 · Quadratic Equation is a polynomial equation of degree two represented as ax2 + bx + c = 0, and its solutions are known as its roots. Learn the formulas and methods of solving quadratic equations with the help of examples at GeeksforGeeks.
The formula to find the roots of the quadratic equation is x = [-b ± √(b 2 - 4ac)]/2a. The sum of the roots of a quadratic equation is α + β = -b/a. The product of the Root of the quadratic equation is αβ = c/a. The quadratic equation whose roots are α, β, is x 2 - (α + β)x + αβ = 0.
Then the formula will help you find the roots of a quadratic equation, i.e. the values of x where this equation is solved. The quadratic formula. x = − b ± b 2 − 4 a c 2 a. It may look a little scary, but you’ll get used to it quickly! Practice using the formula now. Worked example.
Quadratic Equation in Standard Form: ax 2 + bx + c = 0; Quadratic Equations can be factored; Quadratic Formula: x = −b ± √(b 2 − 4ac) 2a; When the Discriminant (b 2 −4ac) is: positive, there are 2 real solutions; zero, there is one real solution; negative, there are 2 complex solutions
Google Classroom. Learn how to solve quadratic equations like x^2=36 or (x-2)^2=49. What you should be familiar with before taking this lesson. Square roots. Special products of binomials. What you will learn in this lesson.
Solve these linear equations and get two roots of the given quadratic equation. Solve \ (x^2 - x - 6 =0 \) by the method of factoring. We have \ [ x^2 - x - 6 = (x-3) (x+2),\] which gives \ ( x = 3 \) or \ ( x = -2 \). \ (_\square\) Note that the factors of \ ( x^2 - x - 6 \) are \ (1, x^2 - x - 6, x-3,\) and \ (x+2\).
3 days ago · A quadratic equation has two roots which may be unequal real numbers or equal real numbers, or numbers which are not real. If a quadratic equation has two real equal roots α, we say the equation has only one real solution. Example: Let 3x 2 2 + x - 2 = 0 be a quadratic equation. Clearly, 3 ∙ (-1) 2 2 + (-1) - 2 = 0.
