Q10 of 242 Page 8

Find the roots of the following quadratic (if they exist) by the method of completing the square.

We have to make the quadratic equation a perfect square if possible or sum of perfect square with a constant.


(a + b)2 = a2 + 2ab + b2



⇒ x2 – 2 × 2ax + 4a2 = b2


⇒ (x – 2a)2 = b2


⇒ x – 2a = ±b


⇒ x = 2a + b, 2a – b

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Find the roots of the following quadratic (if they exist) by the method of completing the square.

 9

Find the roots of the following quadratic (if they exist) by the method of completing the square.

 1

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(i)


(ii)


(iii)


(iv)


(v)


(vi)

2

In the following determine whether the given quadratic equations have real roots and if so, find the roots:

(i)


(ii)


(iii)


(iv)


(v)


(vi)


(vii)


(viii)


(ix)


(x)


(xi)


(xii)