Q. 284.6( 7 Votes )

Solve each of the following quadratic equations:

x2 – 3√5x + 10 = 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 = 1 ;b = -3√5 ;c = 10


= 1.10 = 10


And either of their sum or difference = b


= -3√5


Thus the two terms are -2√5 and -√5


Sum = -2√5-√5 = -3√5


Product = -2√5. -√5 = 2.5 = 10 using 5 = √5. √5




(On using: 10 = 2.5 = 2.√5 √5)


x(x-2√5)-√5 (x-2√5) = 0


(x-√5)(x-2√5) = 0


(x-√5) = 0 or (x-2√5) = 0


x = √5 or x = 2√5


Hence the roots of equation are √5 or 2√5


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