Question

$if \: n \: and \: m \: are \: the \: zeroes \: of \: polynomial \: 3x {}^{2} + 11x - 4 \: find \: the \: value \: of \: \frac{n}{m} + \frac{m}{n}$
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Answer 1

GOOD MORNING!!

Given Quadratic polynomial is

P(x) = 3x² + 11x - 4

It's two zero's are given as m and n

m + n = -11/3 And m × n = -4/3

Find n/m + m/n

n/m + m/n = ( n² + m² )/mn

( n² + m² )/mn ={ ( m + n )² - 2mn }/mn

( n² + m² )/ mn = {(-11/3)² - 2(-4/3) }/-4/3

( n² + m² )/mn = { -(121+24) }/12

( n² + m² )/mn = - 145/12