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Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. Sqrt3x^2+10x+7sqrt3=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.

sqrt3x^2+10x+7sqrt3=0

Solution

We have been given that,

sqrt3x^2+10x+7sqrt3=0

Now divide throughout by sqrt3. We get,

x^2+10/sqrt3x+7=0

Now take the constant term to the RHS and we get

x^2+10/sqrtx=-7

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

x^2+10/sqrt3x+(10/(2sqrt3))^2=(10/(2sqrt3))^2-7

x^2+(10/(2sqrt3))^2+2(10/(2sqrt3))x=16/12

(x+10/(2sqrt3))^2=16/12

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+10/(2sqrt3)=+-4/(2sqrt3)

x=-10/(2sqrt3)+-4/(2sqrt3)

Now, we have the values of ‘x’ as

x=-10/(2sqrt3)+4/(2sqrt3)=-sqrt3

Also we have,

x=-10/(2sqrt3)-4/(2sqrt3)=-7/sqrt3

Therefore the roots of the equation are -sqrt3 and -7/sqrt3.

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Solution Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. Sqrt3x^2+10x+7sqrt3=0 Concept: Solutions of Quadratic Equations by Completing the Square.
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