If {21/4} is the solution set of a quadric equation, find

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If {2¹/₄} is the solution set of a quadric equation, find that equation .

1. 4x² - 9x + 2 = 0
2. 2x² - 9x + 4 = 0
3. x² -18x - 6 = 0
4. 2x² - 18x + 3 = 0
5. None of the above

Correct Option: A

Let α = 2, β = 1/4
Then, α + β = 2 + 1/4 = 9/4
αβ = 2.1/4 = 1/2
Equation having the roots α and β is
x² - (α + β)x + α β = 0
⇒ x² - 9/4x + 1/2 = 0
⇒ 4x² - 9x + 2 = 0