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Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. X2 - 4ax + 4a2 - B2 = 0 - CBSE Class 10 - Mathematics

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Question

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

x2 - 4ax + 4a2 - b2 = 0

Solution

We have to find the roots of given quadratic equation by the method of completing the square. We have,

x2 - 4ax + 4a2 - b2 = 0

Now shift the constant to the right hand side,

x2 - 4ax = b2 - 4a2

Now add square of half of coefficient of x on both the sides,

x2 - 2(2a)x + (2a)2 = b2 - 4a2 + (2a)2

We can now write it in the form of perfect square as,

(x - 2a)2 = b2

Taking square root on both sides,

`(x-2a)=sqrt(b^2)`

So the required solution of x,

x = 2a ± b

x = 2a + b, 2a - b

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Solution Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. X2 - 4ax + 4a2 - B2 = 0 Concept: Solutions of Quadratic Equations by Completing the Square.
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