Question

If a and B are the zeroes of the polynomial x2 - 3x + 2 then find the polynomial whose zeroes are 1/a and 1/B.​

Answer 1

Answer:

$2 {x}^{2} - 3x + 1 = 0$

Step-by-step explanation:

$\alpha + \beta = 3 \\ \\ \alpha \beta = 2 \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } = \frac{3}{2} \\ \\ \frac{1}{ \alpha \beta } = \frac{1}{2} \\ \\ {x}^{2} - \frac{3x}{2} + \frac{1}{2} = 0 \\ \\ 2 {x}^{2} - 3x + 1 = 0$