If roots of ax² + bx + c = 0 are reciprocals of roots of 2x² - 3x + 1 = 0 then a : b : c?
- 1:-2:3
- 2:-3:1
- 1:-3:2
- Nine of these
Explanation
For 2x² - 3x + 1 = 0:
Sum = 3/2, Product = 1/2
Let roots be α, β. Then new roots are 1/α, 1/β
New sum = 1/α + 1/β = (α + β)/αβ = (3/2) / (1/2) = 3
New product = 1/αβ = 1/(1/2) = 2
New equation: x² - (sum)x + product = x² - 3x + 2 = 0
So a:b:c = 1:-3:2
Last verified on 06-05-2026
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