The roots of the equation 4x

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The roots of the equation 4x - 3 × 2^x × 2² + 32 = 0 would include :

1. 1, 2 and 3
2. 1 and 2
3. 1 and 3
4. 2 and 3

Correct Option: D

According to question , we have
Given equation is :- 2^2x - 3 × 2^x × 2² + 32 = 0
⇒ 2^2x - 12 × 2^x + 32 = 0
⇒ y² - 12y + 32 = 0, where 2^x = y
⇒ ( y - 8 ) ( y - 4 ) = 0
⇒ y = 8, y = 4
∴ 2^x = 8 or, 2^x = 4
⇒ 2^x = 2³ or, 2^x = 2²
⇒ x = 3 or, x = 2.
Therefore , the roots of the equation are 3 and 2.