Question

if a and b arexeros of qif a and b arexeros ofusdratic polynomial 3x²-2x-7 find the value of a/b+b/a​

Answer 1

Step-by-step explanation:

$\\ 3 {x}^{2} - 2x - 7 = 0 \\ \\ a + b = \frac{2}{3} \\ \\ ab = - \frac{7}{3} \\ \\ \frac{a}{b} + \frac{b}{a} = \frac{ {a}^{2} + {b}^{2} }{ab} \\ \\ = \frac{ {(a + b)}^{2} - 2ab }{ab} \\ \\ = \frac{ \frac{4}{9} - 2 \times - \frac{7}{3} }{ - \frac{7}{3} } \\ \\ = \frac{ \frac{4}{9} + \frac{14}{3} }{ - \frac{7}{3} } \\ \\ = \frac{ \frac{4 + 42}{9} }{ - \frac{7}{3} } \\ \\ \\ = \frac{46}{9} \times \frac{ - 3}{7} \\ \\ = - \frac{46}{21}$