Miscellaneous Exercise 2

I have Learnt

$ax^2 + bx + c = 0, a \neq 0$ is standard form of quadratic equation in one variable $x$ . There are three methods for solving a quadratic equation. i. Factorization Method ii. Completing Square Method iii. The Quadratic Formula. Some equations are not quadratic but they can be reduced in quadratic form. In the quadratic formula, the expression under the radical sign $b^2 - 4ac$, is called the discriminant. The discriminant tells the nature of roots of quadratic equation. Sum of the roots of a quadratic equation $=S=\frac{b}{a}=\frac{\text{coefficient of }x}{\text{coefficient of }{x}^2}$$= S = \frac{b}{a} = \frac{\text{coefficient of } x}{\text{coefficient of } x^2}$. Product of roots of a quadratic equation $=P=\frac{c}{a}=\frac{\text{constant term}}{\text{coefficient of }{x}^2}$$= P = \frac{c}{a} = \frac{\text{constant term}}{\text{coefficient of } x^2}$. Formula used to form a quadratic equation when its roots are given is $x^2 - Sx + P = 0$. A system of equations having a common solution is called a system of simultaneous equations. The set of all the ordered pairs $(x,y)$ which satisfies the system of equations is called the solution of the system.

MISCELLANEOUS EXERCISE-2

1. Encircle the correct option in the following.