Question

Find the equation whose roots are 3 and1 /3

Answer 1

Answer:

3X² - 10X + 3

Step-by-step explanation:

$let \: \alpha = 3 \\ let \: \beta = \frac{1}{3} \\ \\ sum \: of \: roots \: = \alpha + \beta \\ = 3 + \frac{1}{3} \\ = \frac{9}{3} + \frac{1}{3} \\ = \frac{10}{3} \\ \\ product \: of \: roots \: = ( \alpha )( \beta ) \\ = 3 \times \frac{1}{3} \\ = 1 \\ \\ required \: equation \: = {x}^{2} - (sum \: of \: roots)x \: + (product \: of \: roots) \\ = {x}^{2} - \frac{10}{3} x + 1 \\ \\ to \: convert \: all \: terms\: to \: integers \: \\ multiply \: the \: equation \: by \: 3 \\ 3( {x}^{2} - \frac{10}{3} x + 1) \\ = (3) ({x}^{2} ) - (3)( \frac{10}{3} x) + (3)(1) \\ = 3 {x}^{2} - 10x + 3 \\ \\ final \: equation \: = 3 {x}^{2} - 10x + 3$