Q. 404.0( 17 Votes )

Solve each of the following quadratic equations:

4x2 + 4bx - (a2 - b2) = 0

Answer :


Using the splitting middle term - the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 4 b = 4b c = - (a2 - b2)


= 4. - (a2 - b2)


= - 4a2 + 4b2


And either of their sum or difference = b


= 4b


Thus the two terms are 2(a + b) and - 2(a - b)


Difference = 2a + 2b - 2a + 2b = 4b


Product = 2(a + b). - 2(a - b) = - 4(a2 - b2)


using




2x[2x + (a + b)]-(a-b) [2x + (a + b)] = 0


[2x + (a + b)] [2x-(a-b)] = 0


[2x + (a + b)] = 0 or [2x-(a-b)] = 0



Hence the roots of equation are


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