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

[tex]2 {x}^{2} + 18x + 36 = 0[/tex]
a. 6

b. -6

c. 3

d. -3..​

Respuesta :

altavistard

Answer:

The roots are {-6, -3}

Step-by-step 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}

DᴀʀᴋPᴀʀᴀᴅᴏx

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The Correct choices are ~

b and d

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve ~

  • [tex]2 {x}^{2} + 18 {x}^{} + 36 = 0[/tex]

  • [tex]2 {x}^{2} + 12x + 6x + 36 = 0[/tex]

  • [tex]2x(x + 6) + 6(x + 6) = 0[/tex]

  • [tex](2x + 6)(x + 6) = 0[/tex]

There's two cases here,

Case # 1 - when 2x + 6 = 0

  • [tex]2x + 6 = 0[/tex]

  • [tex]2x = - 6[/tex]

  • [tex]x = - 6 \div 2[/tex]

  • [tex]x = - 3[/tex]

Case # 2 - when x + 6 = 0

  • [tex]x + 6 = 0[/tex]

  • [tex]x = - 6[/tex]

Hence, the roots are -3 and -6 ~

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