Question

Solve the following quadratic equation by completing the square method
3x² +11x +10 = 0​

Answer 1

3x²+6x+5x+10

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

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

Answer 2

Given:-

• 3x² + 11x + 10 = 0

To find:-

• Find the roots of the equation.?

Solutions:-

=> 3x² + 11x + 10 = 0

Now, divide throughout by 3. we get,

=> x² + 11x/3 + (11/6)² = (11/6)² - 10/3

=> x² + (11/6)² + 2(11/6)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, the value of x.

=> x = -11/6 + 1/6

=> x = -5/3

Also,

=> x = -11/6 - 1/6

=> x = -12/6

=> x = -2

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