Question

Form a polynomial whose zeroes are reciprocal of zeroes of 6x² - 7x + 2.

Answer 1

Answer:

$2 {x}^{2} - 7x + 6 = 0.$

Step-by-step explanation:

$6 {x}^{2} - 7x + 2 = 0 \\ \\ \alpha + \beta = \frac{7}{6} \\ \\ \alpha \beta = \frac{2}{6} = \frac{1}{3} \\ \\s = \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } = \frac{ \frac{7}{6} }{ \frac{1}{3} } = \frac{7}{2} \\ \\p = \frac{1}{ \alpha \beta } = 3 \\ \\ \\ \\ {x}^{2} - sx + p = 0 \\ \\ {x}^{2} - \frac{7x}{2} + 3 = 0 \\ \\ 2 {x}^{2} - 7x + 6 = 0.$