Solve each of the following quadratic equations:

x^{2} – 3√5x + 10 = 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 = -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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