Note-(1)An equation of degree 2 is called a quadratic equation.
Ex-1.x²+5x+6=0
2.x²+7x+10=0
3.x²-5x+10=0
4.2x²+8x+6=0
Solution or roots of a quadratic equation:- If p(x)=0 is a quadratic equation,then the zeros of the polynomial p(x) are called the solutions or roots of the quadratic equation p(x)=0.
Note:-1.Since the degree of a quadratic equation is 2,it has 2 roots or solutions.
2.x=a is the root of p(x)=0,if p(a)=0.
Method of solving a quadratic equation-
(a)spliting the middle term:-
1. x²+5x+6=0.
split the middle term 5x=3x+2x ,because multiplication of extreme terms(x²×6)=6x²=3x×2x.
Here x²+3x+2x+6=0
⇒ x(x+3)+2(x+3)=0
⇒(x+3)(x+2)=0
⇒x=-3 ,-2
2. x²-7x+12=0
⇒x²-4x-3x+12=0, because multiplication of extreme term x²×12=(-4x)(-3x)=12x²
⇒x(x-4)-3(x-4)=0
⇒(x-4)(x-3)=0
⇒x=4, 3
3. 2x²+12x+16=0
⇒2x²+8x+4x+16=0
⇒2x(x+4)+4(x+4)=0
⇒(x+4)(2x+4)=0
⇒x=-4 ,-2
solve the following quadratic equation.
1.x²+5x+4=0
2.x²-5x+4=0
3.x²+5x-6=0
4.x²-5x-6=0
