2016 · Q14
If α and β are the two zeros of the polynomial 25x² − 15x + 2, then what is a quadratic polynomial whose zeros are (2α)⁻¹ and (2β)⁻¹?
Elementary MathematicsAlgebra
- Ax²+30x+2
- B8x²-30x+25
- C8x²-30x
- Dx²+30x
Explanation
Here α+β = 15/25 = 3/5 and αβ = 2/25. The new zeros 1/(2α), 1/(2β) have sum (α+β)/(2αβ) = (3/5)/(4/25) = 15/4 and product 1/(4αβ) = 25/8. Hence the polynomial is x²−(15/4)x+25/8 = 0, i.e. 8x²−30x+25 = 0 (option B).