Question

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

Answer 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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Answer 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.