Question

`25x^2+30x+7=0`

Answer 1

Given: 

`25x^2+30x+7=0` 

On comparing it with `ax^2+bx+x=0` 

a = 25,b = 30 and c = 7
Discriminant D is given by: 

`D=(b^2-4ac)` 

=`30^2-4xx25xx7` 

=`900-700` 

=`200` 

=`200` 

=`200>0` 

Hence, the roots of the equation are real.
Roots α and β are given by: 

`α=(-b+sqrt(D))/(2a)=(-30+sqrt(200))/(2xx25)=(-30+10sqrt(20))/50=(10(-3+sqrt(2)))/50=((-3+sqrt(2)))/5` 

`β=(-b-sqrt(D))/(2a)=(-30-sqrt(200))/(2xx25)=(-30-10sqrt(20))/50=(10(-3-sqrt(2)))/50=((-3-sqrt(2)))/5` 

Thus, the roots of the equation are `((-3+sqrt(2)))/5` and `((-3-sqrt(2)))/5`