Question

If m and n are the zeroes of the polynomial 3x^2 +11x−4, find the values of n/ m ​ + m/ n ​

Answer 1

Step-by-step explanation:

$3 {x}^{2} + 11x - 4 = 0\\3 {x}^{2} + 12x - x - 4 = 0 \\ 3x(x + 4) - 1(x + 4) = 0 \\ (3x - 1)(x + 4) = 0 \\x= \frac{1}{3} \: \: \: , \: \: \: -4 \\ so, m= \frac{1}{3} \: \: , \: \: n=-4 \\ \frac{n}{m} + \frac{m}{n} = \frac{ - 4}{ \frac{1}{3} } + \frac{ \frac{1}{3} }{ - 4} \\ = - 12 - \frac{1}{12} \\ = \frac{ - 144 - 1}{12} \\ = \frac{ - 145}{12} \\ \: \boxed{\frac{n}{m} + \frac{m}{n} = \frac{ - 145}{12} } \\ \\ \red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$