Question

Solve the equation

${x}^{2} + 3x + 2 = 0$
​

Answer 1

${x^2+3x+2=0}$

${x^2+2x+x+2=0}$

${x(x+2)+1(x+2)=0}$

${(x+2)(x+1)=0}$

${Now,}$ ${x+2=0}$

${x = -2}$

${Again}$ ${x+1=0}$

${x = -1}$

${Therefore\:, x = -1, -2}$

Answer 2

Hello mate

${\huge{\mathfrak{\red{G}{iven}}}}$

${x^2+3x+2=0}$

${\huge{\mathfrak{\red{T}{o\:find}}}}$

The roots of the above quadratic equation

${\huge{\mathfrak{\red{B}{rainliest\:answer}}}}$

Quadratic equation could be factorised in three ways

1. Splitting middle term method
2. Squaring method
3. Quadratic formula method

Using Splitting middle term method :-

Now,

${x^2+3x+2=0}$

The factors of constant term is 2 and 1

Here, 2 and 1 when added gives the coefficient term of ${x}$

Therefore, we can split 3x as 2x and x

-» ${x^2+2x+x+2=0}$

Taking common factors :-

-» ${x(x+2)+1(x+2)=0}$

Now, taking (x+2) as common , we get

-» ${(x+2)(x+1)=0}$

Since, both the terms equals to zero, each term also equals to zero.

Therefore, Case 1 :-

${x + 2 = 0}$

${x = -2}$

Case 2 :-

${x + 1 = 0}$

-» ${x = -1}$

Therefore, the roots are -2 and -1

Verification :-

Sum of roots = -2 + (-1)

Sum of roots = -2 - 1

Sum of roots = -3.....(1)

Product of roots = (-2)(-1)

Product of roots = 2......(2)

Now, The general for of quadratic equation is

${x^2 - (Sum\:of\:roots)x + (Product\:of\:roots)=0}$

-» ${x^2 - (-3)x + 2=0)}$[From (1)&(2)]

-» ${x^2 + 3x + 2 =0}$

Hence verified.

${\huge{\mathfrak{Be\:Brainly}}}$