## Algebric Expressions

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Algebric Expressions and Inequalities:- Unknown quantities used in any equation are known as variables, generally denoted by x, y, z etc. An equation is a statement of equality of two algebraic expression, which involve one or more unknown quantities, called the variables. Linear equation involves one variable, Quadratic equation involves two variables. The graph of a linear equation is a straight line in X-Y plane. The linear equation is ax+b=c, a #o,  => ax=c-b Hence the value of x = Ex-Solve 2x-7=1
• 2x = 7+1 =8 => x=4.
Quadratic equation general form is ax2 +bx+c=0, a # 0, a, b, c are real numbers.
• ax2 +bx=-c => x2+ baX = - ca => x2+x +)2= -  +  )2
• x =, If one root is α, other root is β.
b2-4ac is called discriminant i.e D Rules- Sum of roots α+β =  ,  Product of root’s = αβ = Example- Solve-2x2+6 = 7x Sol-2x2-7x+6=0    =>2x2-4x-3x+6=0 =>2x(x-2)-3(x-2)=0   =>(x-2)(2x-3)=0   =>x=2 and 2x=3 i.e. x=. Quadratic Equation with given roots:- An equation whose roots are α and β  is (x-α)(x-β) = 0. Or  x2 + (α + β)x + αβ =0 Condition of a Common root between two quadratic equations: ax2 +bx +c =0, dx2 + ex + f =0 are two quadratic equations Let α be a common root of two equation. Hence aα2+bα + c = 0 and dα2 +eα +f = 0
• α2 / bf-ec =  α /cd-fa  =1 / ae – db , Hence two roots.
Inequqtions: A statement or equation which states that one thing is not equal to another, is called an inequation. Symbols. <  shows less than.,   >  represents greater than, . Properties. Adding the same number to each side of an equation does not effect the sign of inequality. Ex-If x > y then x + a > v + a Subtracting the same number to each side of an inequation does not effect the sign of inequality. Ex- If x<y then x – a < y – a Multiplying each side of an inequality with same number does not effect the sign of inequality. Ex-If x  y then ax    ay ( where a > 0)