Question

If 2 and 3 are the zeros of polynomial 3x^2-2kx+2m then find the values of k and m

Answer 1

Answer:

if two and three other zeros of the polynomial 3 x square - 2K x + 2 m then

1) 3(2^3)-2k(2)+2m =0

=> 24-4k +2m = 0

=> m-2k = -12

2) 3(3)^3 -2k(3) +2m=0

=> 81-6k+2m = 0

=> 2m-6k = -81

now there are two equations in two variables you can easily solve this

hope it works ❤️

plz mark it as brainliest answer

Answer 2

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$If \ 2\ and \ 3 \ are\ the\ zeros\ of \ polynomial\\ 3x^2-2kx+2m \ then \ find\ the\ values \\ of \ k \ and\ m$

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☆《2,3 are the zeroes of p(x), so p(2) = p(3) = 0》☆

$\boxed{\red{\bold{Solving \ for \ p(2):}}}$

$\purple{\implies p(x)=3x^2 -2kx +2m}$

$\purple{\implies}p(2) = 3(2)^2 -2k(2)+2m = 0$

$\purple{\implies}12 - 4k +2m = 0$

$\purple{\implies}m-2k =-6 \ \; \; - (i)$

$\boxed{\red{\bold{Solving \ for \ p(3):}}}$

$\blue{\implies p(x) = 3x^2 -2kx +2m}$

$\blue{\implies}p(3)=3(3)^2 -2(3)k+2m = 0$

$\blue{\implies}27 - 6k + 2m =0$

$\blue{\implies}m-3k = \displaystyle{\frac{-27}{2}}\ \; \; - (ii)$

$\boxed{\red{\bold{Subtracting \ both\ equations:}}}$

$\green{\implies m-2k - (m-3k) = -6 - \displaystyle{\frac{-27}{2}}}$

$\green{\implies}m-2k-m+3k =-6+13.5$

$\green{\boxed{\implies{\boxed{k = 7.5}}}}$

$\green{\boxed{\implies{\boxed{m= 2k-6 = 2(7.5 - 3) = 9}}}}$

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