If 2 and 3 are the zeros of polynomial 3x²-2kx+2m.find the value of k

1.	If 2 and 3 are the zeros of polynomial 3x²-2kx+2m.find the value of k and m?
Answer» Let p(x) = 3x²-2kx+2mGiven, 2 & 3 are zeroes of p(x).Then , p (2) = 0 & p(3)= 0Now, p(2)= 3×2²-2k(2)+2m=03× 4-4kx+2m=012-4k+2m=0………..(1)p(3) = 3×3²-2k(3)+2m=03× 9-6kx+2m=027-6k+2m=0………..(2)On Subtracting Equation 1 from equation 2.27-6k+2m=012-4k+2m=0(-) (+) (-)------------------15-2k =015=2kk= 15/2On putting k= 15/2 in eq 112-4k+2m=012-4(15/2)+2m=012-30+2m=0-18+2m=02m=18m=18/2m=9Hence, k=15/2, m= 9

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