Question

if m and n are the zeros of the polynomial
$3 {x }^{2} + 11x - 4$
Then find the value of m /n + n/m​

Answer 1

We have,

p(x)=3x²+11x-4

Given that m and n are the zeros of the above polynomial

Here,

m+n= -11/3 and mn= -4/3

To find: m/n + n/m

Now,

m²+n²

=(m+n)²-2mn

= (-11/3)² -2(-4/3)

=121/9+8/3

=145/9

Thus,

m/n + n/m

»(m²+n²)/mn

»(145/9)/(-4/3)

»145/9 × -3/4

» -145/12