Question

if m and n are zeroes of polynomial 3x²+11x-4 then the value of m/n+n/m ​

Answer 1

Answer:

Given:

m and n are the zeroes of the polynomial as follows:

3x² + 11x - 4 = 0

To find:

Value of m/n + n/m

Concept:

First by middle term factorisation, we shall get the zeroes of the given polynomial.

Calculation:

3x² + 11x - 4 = 0

=> 3x² + 12x - x - 4 = 0

=> 3x(x + 4) -1(x + 4) = 0

=> (3x - 1)(x + 4) = 0

So, 3x - 1 = 0

=> x = ⅓........(1)

Similarly,

x - 4 = 0

=> x = -4 .........(2)

Let m be ⅓ and n be (- 4)

As per the question

m/n + n/m

=( ⅓/-4 ) + (-4/⅓)

= (-1/12) + (-12)

= (-1 - 144)/12

= -145/12

So the final answer is (-145/12)

Answer 2

Question :

If m and n are zeroes of the polynomial 3x²+11x-4 then the value of m/n+n/m.

Answer

$3 {x}^{2} + 11x - 4$

$3 {x}^{2} + 12 x - 1x - 4 \\ \\ 3x(x + 4) - 1(x + 4) \\ \\ (3x - 1)(x + 4)$

Now take

3x-1=0 and x+4=0

3x=1 and x=-4

x=1/3 and x=-4

Consider , x=1/3=m and x= -4 =n

Now, Put the value of m and n in given condition,

We get,

$\frac{ \frac{1}{3} }{ - 4} + \frac{ - 4}{ \frac{1}{3} } \\ \\ \frac{1}{ - 12} + (- 12) \\ \\ \frac{1 }{-12} - 12 \\ \\ \frac{ 1+ 144}{-12} \\ \\ -\frac{145}{12}$

hence the answer is -145/12