Question

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

Answer 1

GIVEN
P(x) = 3x^2 + 11 x - 4
Now make P(x) = 0
Therefore, 3x^2 + 11 x - 4 = 0
Factorize
3x^2 + 12x -x - 4 = 0
3x (x + 4) - 1 (x + 4) = 0
(3x - 1) (x + 4) = 0
3x - 1 = 0 & x + 4 = 0
3x = 1 & x = - 4
x = 1 / 3 & - 4
Assume 1 / 3 as m and - 4 as n
FIND
m/n +n/m
Subsitute m and n value
[(1 / 3) / (- 4)] + [(- 4) / (1 / 3)]
= [(1 / 3) / (- 4 / 1 )] + [(- 4 / 1) / (1 / 3)]
= (- 1 / 1 2) + (- 12)
= (- 1 / 1 2) - 12
LCM is 12
(- 1 - 144) / 12
= - 145 / 12
This is your desired answer.

Answer 2

given,
zeroes of the polynomial 3x²+11x -4  are m and n
⇒ 3(m)² + 11(m) -4 = 0
⇒ 3m²+ 11m -4 = 0
⇒ 3m² +12m -m - 4 = 0
⇒3m( m+ 4) - 1( m + 4)  =0
⇒ (3m - 1) ( m+4) = 0
⇒ (3m - 1) = 0 (or) (m +4 ) = 0
⇒ m = 1/3 or m = -4
if we replace n in x place , we get the same values
Hence , m/n + n/m = 1 + 1 =2

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