Solution of Quadratic Equations
To find the solution set of a quadratic equation, following methods are used:
- factorization
- completing square
- use of quadratic formula
To find the solution set of a quadratic equation, following methods are used:
An equation of 2nd degree is called quadratic equation. In more detail, the quadratic equation is an equation, which contains the square of the unknown (variable) quantity, but no higher power. General or standard form of a quadratic equation: A 2nd degree equation in one variable x of the form as below, where a ≠ 0…
In this method, write the quadratic equation in the standard form as ax2 + bx + c = 0 (i) If two numbers r and s can be found for the equation (i) such that r + s = b and rs = ac then ax2 + bx + c can be factorized into two…
Generally, we presume that most chemical and physical changes proceed to completion. A complete reaction is one in which all reactants have been converted into products. However, most chemical reactions do not go to completion because products react themselves to form the reactants. As a result, after sometime no further change takes place. Quantities of…
Question 1. Find the order of the following matrices. Solution: $$ A = \begin {bmatrix} 2 & 3 \\ -5 & 6 \\ \end{bmatrix} $$ Order of matrix A is 2-by-2 $$ B = \begin {bmatrix} 2 & 0 \\ 3 & 5 \\ \end{bmatrix} $$ Order of matrix B is 2-by-2 $$…
The matrices and determinants are used in the field of Mathematics, Physics, Statistics, Electronics and other branches of science. The matrices have played a very important role in this age of computer science. The idea of matrices was given by Arthur Cayley, an English mathematician of nineteenth century, who first developed, “Theory of Matrices” in…
Question 1. Write the following quadratic equations in the standard form and point out pure quadratic equations. $ \pmb{ (i). \;\;\;\;\; (x + 7) (x − 3) = -7} $ Solution: The given quadratic equation is $$ (x + 7) (x − 3) = -7 \;\;\;\;\; (i) $$ Multiplying the expressions $ (x + 7)…
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