Answer :



taking LCM





x + 4 = 2x2 + 3x cross multiplying


2x2 + 2x - 4 = 0 taking 2 common


x2 + x - 2 = 0


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 = 1 b = 1 c = - 2


= 1. - 2 = - 2


And either of their sum or difference = b


= 1


Thus the two terms are 2 and - 1


Difference = 2 - 1 = 1


Product = 2. - 1 = - 2


x2 + x - 2 = 0


x2 + 2x - x - 2 = 0


x(x + 2) - (x + 2) = 0


(x + 2) (x - 1) = 0


(x + 2) = 0 or (x - 1) = 0


x = - 2 or x = 1


Hence the roots of equation are - 2 or 1.


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