Q. 724.1( 8 Votes )

Solve each of the following quadratic equations:

4(x + 1) + 4(1 - x) = 10

Answer :

Given: 4(x + 1) + 4(1 - x) = 10

- - - - - - - (1)


Let 4x = y - - - - - - - - - - (2)


substituting for y in (1)


4y2 - 10y + 4 = 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 = 4 b = - 10 c = 4


= 4.4 = 16


And either of their sum or difference = b


= - 10


Thus the two terms are - 8 and - 2


Sum = - 8 - 2 = - 10


Product = - 8. - 2 = 16


4y2 - 10y + 4 = 0


4y2 - 8y - 2y + 4 = 0


4y(y - 2) - 2(y - 2) = 0


(y - 2) (4y - 2) = 0


(y - 2) = 0 or (4y - 2) = 0


y = 2 or y = 1/2


substituting the value of y in (2)


4x = 2 or 4x = 2 - 1


22x = 21 or 22x = 2 - 1


2x = 1 or 2x = - 1



Hence the roots of equation are


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