If m & n are the 0's of the polynomial 3x 2 +11x-4. Find m/n + n/m.
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m,n are the zeros of 3x²+11x-4=0
then, m+n=-11/3 and m.n=-4/3
∴, m/n+n/m=(m²+n²)/mn={(m+n)²-2mn}/mn={(-11/3)²-2.(-4/3)}/-4/3
=(121/9+8/3)/-4/3=-{(121+24)/9}/4/3=-(145/9)/4/3=-(145/9)×(3/4)
=145/12
then, m+n=-11/3 and m.n=-4/3
∴, m/n+n/m=(m²+n²)/mn={(m+n)²-2mn}/mn={(-11/3)²-2.(-4/3)}/-4/3
=(121/9+8/3)/-4/3=-{(121+24)/9}/4/3=-(145/9)/4/3=-(145/9)×(3/4)
=145/12
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