Solve the equation 3x² – 14x + 8 = 0 when
1. x ∈ N
2. x ∈ Q
______________​

2 thoughts on “Solve the equation 3x² – 14x + 8 = 0 when<br />1. x ∈ N<br />2. x ∈ Q<br />______________​”

1. Given : 3x² – 14x + 8 = 0

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   ➳ 3x² – 14x + 8 = 0

   ➳ 3x² – 12x – 2x + 8 = 0

   ➳ 3x (x – 4) – 2 (x – 4) = 0

   ➳ (x – 4) (3x – 2) = 0 (Factorising left side)

   ➳ x – 4 = 0 or 3x – 2 = 0 (Zero – product rule)

   ➳ x = 4 or x = 2/ 3

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   ❶ When x ∈ N :

   ➢ As 4 ∈ N and 2/3 ∉ N,

   ☆ Therefore,

   • The given equation has 4 as its roots.

   ❷ When x ∈ Q :

   ➢ As 4, 2/3 ∈ Q,

   ☆ Therefore,

   • The given equation has 4, 2/3 as its roots.

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2. Solution:–

   => 3x²-14x+8=0

   => 3x²-12x-2x+8=0

   => 3x(x-4)-2(x-4)=0

   => (3x-2)(x-4)=0

   => x=2/3 and x=4

   => When x ∈ N

   As 4 ∈N and 2/3 not belongs to N

   Therefore

   • The equation has 4 as it’s root.

   => When x ∈ Q

   As 4,2/3 ∈ Q

   Therefore

   • The equation has 4, 2/3 as it’s roots.

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