Question

Find the roots of quadratic equation by factorization - x^2 - 2ax +a^2-b^2

Answer 1

Answer:

I hope you are satisfied with my solution

Answer 2

Answer:

x^2 - 2ax + a^2 - b^2

Splitting the middle term( coeff. of x ) in such a way that product of those parts will be equal to the product of the coeff.

of x^2 and the constant term.

Here, suitable parts are ( a + b ) and ( a - b ) -

= > x^2 -x( a + b + a - b ) + a^2 - b^2

= > x^2 - ( a + b )x - ( a - b )x + a^2 - b^2

= > x^2 - ( a + b )x - ( a - b )x + ( a + b )( a - b )

= > x( x - a - b ) - ( a - b )( x - a - b )

= > ( x - a - b )( x - ( a - b ) )

= > ( x - a - b )( x - a + b )

= > { x - ( a + b ) } { x - ( a - b ) }

Hence the roots of x^2 - 2ax + a^2 - b^2 are a + b and a - b