b(2)+5b+6=0

Question

b (squared)+5b+6=0

Answer 1

b² + 5b + 6 = 0

This trinomial may be factored as the product of two binomials if we find two numbers such that:

- Their product is equal to 6, and

- Their sum is equal to 5

These two numbers indeed exist:

they are 3 and 2: (3)(2) = 6; and (3)+(2) = 5

Then our trinomial factors neatly: (b + 3)(b + 2) = 0

Now, since the product of the 2 binomials is 0, we assume that one or both are equal to 0:

b + 3 = 0   =>  b = -3

b + 2 = 0  =>  b = -2

Then b has two real solutions: -2 and -3.

It's a good habit to check your answers; it allows you to detect any mistakes and correct them before it's too late:

b² + 5b + 6 = 0

* Let's check b = -3:   (-3)² + 5(-3) + 6 = 0   ???

   9 - 15 + 6 = 0   Check!

* So far so good.   Now b = -2:     (-2)² + 5(-2) + 6 = 0    ????

   4 - 10 + 6 = 0   Check!!!  we're correct!  Let's move to the next problem.  No problem!!

 

Answer 2

In order to solve this equation you have to factor.

b^2 + 5b + 6 = 0

(b + 2) (b + 3) = 0

Now what values of b will make this equation true? Remember anything multiplied by 0 = 0.

b = -2 or -3

Here's why. Plug -2 into the equation.

(-2 + 2) (-2 + 3) = 0      Simplify

(0) * (1) = 0

0 = 0                            Answer proven. Now try -3

(-3 + 2) (-3 + 3) = 0      Simplify

(-1) * (0) = 0

0 = 0                            Answer proven.

b = -2 or b = -3

Answer 3

b² + 5b + 6 = 0

The first step that you need to take is factoring the left side

Since the coefficient on the b² term is (understood) 1, the factors will be (1)b and (1)b

(b ? ?)(b ? ?) = 0

Since the constant is 6, the factors will either be 6 and 1 or 2 and 3.  Since the coefficient on the b term is 5 and the sign on the constant is positive, the factors of 6 must add up to 5.  This means that the constants in the factors must be 2 and 3.

(b ? 2)(b ? 3) = 0

Because the sign on the 6 is positive, the signs in the factors have to be the same.  Since the sign on the 5b is positive, the signs must be +.

(b + 2)(b + 3) = 0

Since anything times 0 will equal 0, the statement will be correct if either factor equals =0.

b + 2 = 0                or    b + 3 = 0

b + 2 - 2 = 0 - 2      or    b + 3 - 3 = 0 - 3

b = -2                    or    b = -3

The answers are b = -2 and b = -3.