Q. 454.7( 9 Votes )

Solve each of the following quadratic equations:

x2 + 6x - (a2 + 2a - 8) = 0

Answer :

x2 + 6x - (a2 + 2a - 8) = 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 = 6 ;c = - (a2 + 2a - 8)


= 1. - (a2 + 2a - 8)


= - (a2 + 2a - 8)


And either of their sum or difference = b


= 6


Thus the two terms are (a + 4) and - (a - 2)


Difference = a + 4 - a + 2


= 6


Product = (a + 4) - (a - 2)


= - (a2 + 2a - 8)


x2 + 6x - (a2 + 2a - 8) = 0


x2 + (a + 4)x - (a - 2)x - (a + 4)(a - 2) = 0


x [x + (a + 4)] - (a - 2) [x + (a + 4)] = 0


[x + (a + 4)] [x - (a - 2)] = 0


[x + (a + 4)] = 0 or [x - (a - 2)] = 0


x = - (a + 4) or x = (a - 2)


Hence the roots of equation are - (a + 4) or (a - 2)


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