Followers

Tuesday, February 12, 2019

Quadratic equation


Quadratic equation:-An equation of the form ax²+bx+c=0 where a,b and c ∈ R and a≠0 is called a quadratic equation.

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


Monday, February 11, 2019

Properties of multiplication

Multiplication:-

1.Multiplication of any number by 11:-

   45×11=4 (4+5) 5=495

   25×11=2 (2+5) 5=275

   37×11=3 (3+7) 7=3(10)7=407(Add carry on      next digit).

    123×11=1 (1+2) (2+3) 3=1353.

    217×11=2 (2+1) (1+7) 7=2387.

    531×11=5 (5+3) (3+1) 1=5841.

    679×11=6 (6+7) (7+9) 9=6(13)(16)9=7469.
 
     ( Add carry on next digit).




      Follow on my blogs.