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The number of roots of a polynomial equation is equal to its degree. So, a quadratic equation has two roots. Some methods for finding the roots are: Factorization method; Quadratic Formula; Completing the square method; All the quadratic equations with real roots can be factorized. The physical significance of the roots is that at the roots of ...
For a given quadratic equation ax 2 + bx + c = 0, the values of x that satisfy the equation are known as its roots. i.e., they are the values of the variable (x) which satisfies the equation. The roots of a quadratic function are the x-coordinates of the x-intercepts of the function.
When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive but not a perfect square then the roots of the quadratic equation ax 2 + bx + c = 0 are real, irrational and unequal. Here the roots α and β form a pair of irrational conjugates.
For D > 0, the roots are real and distinct, for D = 0 the roots are real and equal, and for D < 0, the roots do not exist or the roots are imaginary complex numbers. With the help of this discriminant and with the least calculations, we can find the nature of the roots of the quadratic equation.
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.
Jan 24, 2023 · To determine the nature of the roots of any quadratic equation, we use discriminant. Q.4. What are the five real-life examples of a quadratic equation? Ans: Five real-life examples where quadratic equations can be used are (i) Throwing a ball (ii) A parabolic mirror (iii) Shooting a cannon (iv) Diving from a platform (v) Hitting a golf ball
Aug 3, 2023 · The roots of a quadratic equation are the values of the variable that satisfies the equation. They are also known as the ‘zeroes’ of the quadratic equation. For the equation ax 2 + bx + c = 0 the two roots α and β are: α = − b + b 2 − 4 a c 2 a. β = − b − b 2 − 4 a c 2 a.
Dec 13, 2023 · A highly dependable method for solving quadratic equations is the quadratic formula, based on the coefficients and the constant term in the equation. See Example. The discriminant is used to indicate the nature of the roots that the quadratic equation will yield: real or complex, rational or irrational, and how many of each. See Example.
contributed. A quadratic equation is a polynomial equation with degree two. In other words, it is an equation of the form \ ( ax^2 + bx + c =0 \), where \ ( a \), \ (b\) and \ (c\) are real numbers and \ (a\neq 0\). Solving by Factoring. Main Article: Factoring Polynomials. We can solve quadratics using factoring and the zero product property.
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
