Question

if (3x-2) is a factor of 3x^3-kx^2 +21x-10 ,find the value of k

Answer 1

3x-2=0
3x=2
x=2/3

f(x)=3x³-kx²+21x-10
f(2/3)=3(2/3)³-k(2/3)²+21(2/3)-10
       0=3(8/27)-k(4/9)+14-10
k(4/9)=(8/9)+4
k(4/9)=(8+36)/9
     4k=44
       k=44/4
       k=11   

Answer 2

Hii friend,

3X-2 is a factor of the given polynomial.

3X-2 = 0

3X = 2

X = 2/3

P(X) = 3X³-KX²+21X-10

P(2/3) = 3 × (2/3)³ - K × (2/3)² + 21 × 2/3 - 10

= 3×8/27 - K × 4/9 + 14 - 10

= 8/9 - 4K/9 + 4

= 8-4K+36 ÷ 9 = 0

= -4K + 44 = 0

= -4K = -44

K = -44/-4 = 11


Hence,

K = 11


HOPE IT WILL HELP YOU..... :-)