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

Let us compare the given polynomial 3x2+11x 4 with the standard form ax2+ bx+c.

So, we have,Using (1) (2) we get,

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

ans:

here by factor theorm; (x-a) is a factor if f(a)=0

since (x – m) is a zero(factor) comparing it with (x – a) we get;

  a = m

so;

f(m)= 3m2 + 11m -4

or, 0 = 3m2  + 11m – 4

or, 0= 3m2 + 12m – m -4

or, 0= 3m(m + 4) -1(m + 4)

or,0= (3m -1) (m + 4)

either,  either,

0= (3m -1)  (m + 4) = 0

Hence, m= 1/3  hence, m = -4

Or,  0= (3n -1)  or,  (n + 4) = 0

Hence, n= 1/3   hence, n = -4

 

Finally;

m/n + n/m = (1/3)/(-4) + (-4)/(1/3) =  -12 – 1/12 =-145/12



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Hello , by quadratic formula, we have  x = (-11 + 13)/6 or (-11 - 13)/6 = 1/3 or -4

hence , m = 1/3 & n = -4 , therefore  m/n = -(1/12)  and n/m = -12 , therefore  m/n + n/m  = -145/12

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can u explain this quadratic form for me plz

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 If ax2 + bx +c = 0 is a quadratic equation, then its roots can be given by formula : x ={ -b + root(b2 - 4ac)} /2a

or

{-b - root(b2 - 4ac)}/2a

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