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# Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. 3x2 + 11x + 10 = 0 - Mathematics

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#### Question

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

3x2 + 11x + 10 = 0

#### Solution

We have been given that,

3x2 + 11x + 10 = 0

Now divide throughout by 3. We get,

x^2+11/3x+10/3=0

Now take the constant term to the RHS and we get

x^2+11/3x=-10/3

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

x^2+11/3x+(11/6)^2=(11/6)^2-10/3

x^2+(11/6)^2+2(11/3)x=1/36

(x+11/6)^2=1/36

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+11/6=+-1/6

x=-11/6+-1/6

Now, we have the values of ‘x’ as

x=-11/6+1/6=-10/6=-5/3

Also we have,

x=-11/6-1/6=-12/6=-2

Therefore the roots of the equation are -2 and -5/3.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))