## Friday, May 31, 2013

Blog-65

Dear Students,

Following two files are very important to improve your base for remembering the formulas. It is 100 % free for all the students of the world. Download these two files, take the Print Out of these files on two sides of the paper and practice these formulas for your benefit to get high scores in Mathematics Standard 10/ Grade 10.

In the Previous Blog we had seen some important concepts of Quadratic Equation.
2) Click Here to Read the Blog
3) Click Here to Read the Blog
4) Click Here to Read the Blog
5) Click Here to Read the Blog

Some special and critical types of the factors:
Just go through this downloaded file and be prepared to solve any problem pertaining to these critical factors.

Now we will see few quadratic equation using formula method.
a) Solve the quadratic equation  5 x 2 - 2 x - 9 = 0.
Solution:
1) Comparing  5 x 2 - 2 x - 9 = 0 with a x 2 + b x + c = 0 we get,
a = 5, b = - 2, c = - 9

b) Solve the quadratic equation  3 x 2 - 4 x - 3 = 0.
Solution:
1) Comparing  3 x 2 - 4 x - 3 = 0  with a x 2 + b x + c = 0 we get,
a = 3, b = - 4, c = - 3

Now we will see some rules about the roots of the quadratic equation.
1) Sum of the roots (α, β) of the quadratic equation a x 2 + b x + c = 0,
α  +  β  =  - b / a  and   α β  =  c / a
α  +  β  =  - Coefficient of x / Coefficient of x 2  and   α β  =  Constant / Coefficient of x 2.
2) If α, β are the roots of the quadratic equation then the quadratic equation will be
x 2 - (Sum of the roots)  x + (Product of the roots) = 0,
x 2 - (α  +  β)  x + (α β) = 0,

Now we will see some important problems on Quadratic equation and the roots of the Quadratic Equations

a) If the sum of the roots of the quadratic equation is 3 and the sum of their cubes is 63, then find the equation.
Solution:
1)  Here, α + β =  3 and  α 3 + β 3 =  63
2)  We know that , α 3 + β 3 =  (α + β)- 3 α β (α + β)
so ,     63      =  (3)- 3 α β (3)
63      =  27 - 9 α β       Dividing by 9 through out we get
7       =  3  - α β
α β   =  3  - 7
α β   =  - 4
3) We know that  the quadratic equation will be
2 - (α  +  β)  x + (α β) = 0
2 - (3)  x + (- 4) = 0
2 - 3 x - 4 = 0
4)  Answer: So the required quadratic equation will be 2 - 3 x - 4 = 0.
Few more problems will be discussed in the next Blog.