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Let α and β be the roots of x^2 - 3x + p = 0 and γ and δ form a geometric progression. Then ratio (2q + p) : (2q - p) is : (1) 3 : 1 (2) 9 : 7 (3) 33 : 31 (4) 5 : 3

1. 3 : 1
2. 9 : 7
3. 33 : 31
4. 5 : 3

Correct answer: 9 : 7

Solution

The correct option is derived from the relationships between the roots of the quadratic equation and the properties of the geometric progression formed by γ and δ. By applying Vieta's formulas and the conditions of the geometric progression, we can establish the ratio (2q + p) : (2q - p) as 9 : 7.

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