Question

solve the quadratic equation X2+5x+6=0​

Answer 1

Answer:

(x+3)(x+2)=0

or, x=-3 and x=-2

Step-by-step explanation:

We have the Quadratic equation

${x}^{2} + 5x +6 = 0$

We have to factorise this quadratic equation.

As the Highest power of this equation is 2, then its highest number of factors will be 2.

We can compare this equation with the quadratic equation

$a {x}^{2} + bx + c$

Here, a=1, b =5 , c=6.

We have to find out two numbers such that if we multiply them we get 6 and if we add them we get 5.

Such two numbers are 2 and 3.

So we can write the given quadratic equation as

${x}^{2} + (3 + 2)x + 6 = 0$

If we open the bracket, we get,

${x}^{2} + 3x + 2x + 6 = 0$

We can see that, in the first two terms i.e. x² and 3x, x is common and 2 is common in next two terms i.e. 2x and 6.

So by taking x common from first two terms and 2 common from next two terms, we get.

$x(x + 3) + 2(x + 3) = 0$

Now we have two terms and x+3 is common in both terms. So if we take (x+3) common from this two terms, we get,

$(x + 3)(x + 2) = 0$

or,

$(x + 3) = 0 \: or \: (x + 2) = 0$

or,

$x = - 3 \: or \: x = - 2$

Conclusion:

The value of x is either -3 or -2 .

Answer 2

Answer:

x = -2; x = -3

Step-by-step explanation:

The given equation is x² + 5x + 6 = 0

Here, we have two different methods

• Prime factorisation
• Formula method

Prime Factorisation Method:

We need to select two factors such that if we multiply two factors we must get the last term and  if we add them we must get the middle answer which is as follows:

{2 X 3 = 6;  2 + 3 = 5}

x² + 5x + 6 = 0

x² + 2x + 3x + 6 = 0

x( x + 2) + 3 (x + 2) = 0

(x + 2) (x + 3) = 0

x + 2 = 0

x = - 2

x + 3 = 0

x = -3

Thus, x = -2 or -3

Formula Method:

x = -b ± √b² - 4ac/2a

The general form of quadratic equation is ax² + bx + c = 0

a = 1, b = 5, c = 6

x = - 5 ± √5² - 4x1x6 / 2 x 1

x = -5 ± √25 - 24 / 2

x = -5 ± 1 / 2

x = -5 + 1 / 2x = -2

x = -4/2

x = - 2

x = -5 -1 / 2

x = -6/2

x = - 3

Thus, x = -2 or -3.