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# Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. Sqrt2x^2-3x-2sqrt2=0 - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Completing the Square

#### Question

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

sqrt2x^2-3x-2sqrt2=0

#### Solution

We have been given that,

sqrt2x^2-3x-2sqrt2=0

Now divide throughout by sqrt2. We get,

x^2-3/sqrt2x-2=0

Now take the constant term to the RHS and we get

x^2-3/sqrt2x=2

Now add square of half of co-efficient of ‘x’ on both the sides. We have,

x^2-3/sqrt2x+(3/(2sqrt2))^2=(3/(2sqrt2))^2+2

x^2+(3/(2sqrt2))^2-2(3/(2sqrt2))x=25/8

(x-3/(2sqrt2))^2=25/8

Since RHS is a positive number, therefore the roots of the equation exist.

So, now take the square root on both the sides and we get

x-3/(2sqrt2)=+-5/(2sqrt2)

x=3/(2sqrt2)+-5/(2sqrt2)

Now, we have the values of ‘x’ as

x=3/(2sqrt2)+5/(2sqrt2)

x=8/(2sqrt2)=4/(sqrt2)=2sqrt2

Also we have,

x=3/(2sqrt2)-5/(2sqrt2)

x=-1/sqrt2

Therefore the roots of the equation are 2sqrt2 and -1/sqrt2.

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Solution Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. Sqrt2x^2-3x-2sqrt2=0 Concept: Solutions of Quadratic Equations by Completing the Square.
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