Question

the equation 2xsquare+3x+1=0 ​

Answer 1

Using factorization :

Given, 2x² + 3x + 1 = 0

or, 2x² + 2x + x + 1 = 0

or, 2x (x + 1) + 1 (x + 1) = 0

or, (x + 1) (2x + 1) = 0

Either x + 1 = 0 or, 2x + 1 = 0

x = - 1 , x = - 1/2

The required solutions be

         x = -1 , - 1/2

Using Sridhar Acharya's Formula :

Given equation is

2x² + 3x + 1 = 0

Therefore, x = $\frac{-3\pm \sqrt{3^{2}-4*2*1}}{2*2}$

                     = $\frac{-3\pm \sqrt{1}}{4}$

                     = $\frac{-3\pm 1}{4}$

                     = - 1, - 1/2

The required solutions be

          x = -1 , - 1/2

Answer 2

2x²+3x+1=0

2x²+2x+x+1

2x(x+1)+1(x+1)

(2x +1) (x+1)