Question

if m and n are the zeros of the polynomial X square + 11 x minus 4 then find the value of m/n+n/m​

Answer 1

$\huge{\boxed{\text{Answer :-}}}$

♦ Provided in the question

→ "m" and "n" are the zeros of the Polynomial $x^2 + 11x - 4$

♦ Asked in question

→ Find the value of $\dfrac{m}{n} + \dfrac{n}{m}$

♦ Solution :-

>> As we know that

→ Sum of roots = $\dfrac{-b}{a} = (m+n)$

→ $\dfrac{-11}{1} = -11 = (m+n)$

→ Product of roots = $\dfrac{c}{a} = mn$

→ $\dfrac{-4}{1} = -4 = mn$

>> Now by further solving

$\dfrac{m}{n} + \dfrac{n}{m}$

$= \dfrac{m^2}{mn} + {n^2}{mn}$

$= \dfrac{m^2 + n^2}{mn}$

♦ As

$a^2+b^2 = (a+b)^2 - 2ab$

>> Then we can write above's equation as

$\dfrac{(m+n)^2 - 2mn}{mn}$

>> By substituting values of (m+n) and mn

$\dfrac{(-11)^2 - 2(-4)}{-4}$

$= \dfrac{121 + 8}{-4}$

$= \dfrac{129}{-4}$

$= \dfrac{-129}{4}$