Question

If m and n are the zeroes of 3x2 + 11x - 4 find
m/n+n/m​

Answer 1

Answer:

$\large{\underline{\boxed{\sf - \dfrac{145}{12}}}}$

Step-by-step explanation:

Given polynomial;

3x² + 11x - 4, here

• a = 3
• b = 11
• c = - 4

If m and n are the zeroes -

Sum of zeroes = -b/a

⇒ m + n = -11/3

Product of zeroes = c/a

⇒ m * n = -4/3

Now, we have to find ;

$\implies \sf \frac{m}{n} + \frac{n}{m} \\ \\ \implies \sf \frac{m {}^{2} + {n}^{2} }{mn}$

We know that ;

a² + b² = (a + b)² - 2ab

$\implies \sf \frac{ {m}^{2} + {n}^{2} }{mn} \\ \\ \implies \sf \frac{(m +n ) {}^{2} - 2mn}{mn}$

Putting the value of (m + n) and mn,

$\implies \sf \frac{ - ( \frac{11}{3} ) {}^{2} - 2 \times ( - \frac{4}{3} )}{ - \frac{4}{3} } \\ \\ \implies \sf \frac{ \frac{121}{9} + \frac{8}{3} }{ - \frac{4}{3} } \\ \\ \implies \sf \frac{121 + 24}{9} \div ( - \frac{4}{3} ) \\ \\ \implies \sf \frac{145}{9} \times ( - \frac{3}{4} ) \\ \\ \implies \sf - \frac{145}{12}$

Hence, the answer is (-145/12).