Question

Help ! which of the following are the roots of the given quadratic equation ?


`2 {x}^(2) + 18x + 36 = 0`
a. 6

b. -6

c. 3

d. -3..​

Answer 1

The roots are {-6, -3}

Explanation:

We are given four possible roots. To determine whether or not a particular possible root is actually a root, we use synthetic division. If the remainder is zero, we may conclude that this is actually a root.

Determine whether or not -3 is a root. Setting up synthetic division, we get

-3 / 2 18 36

-6 -36

---------------------

2 12 0

Since the remainder is zero, -3 is a root.

Try -6: Is this a root of 2x + 12? Setting up synthetic division, we get

-6 / 2 12

-12

----------------

2 0

The remainder is again zero, so -6 is also a root of the original equation.

The roots are {-6, -3}

Answer 2

`▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪`

The Correct choices are ~

b and d

`\large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}`

Let's solve ~

• 
  `2 {x}^(2) + 18 {x}^{} + 36 = 0`

• 
  `2 {x}^(2) + 12x + 6x + 36 = 0`

• 
  `2x(x + 6) + 6(x + 6) = 0`

• 
  `(2x + 6)(x + 6) = 0`

There's two cases here,

Case # 1 - when 2x + 6 = 0

• 
  `2x + 6 = 0`

• 
  `2x = - 6`

• 
  `x = - 6 / 2`

• 
  `x = - 3`

Case # 2 - when x + 6 = 0

• 
  `x + 6 = 0`

• 
  `x = - 6`

Hence, the roots are -3 and -6 ~