Question

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

3x² + 11x + 10 = 0

Answer 1

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`.