Question

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

Answer 1

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correct question :if (3x-2)is a factor of 3x³-kx²+21x-10,find the value of k

let 3x-2=0

$⟹x = \frac{2}{3}$

sub. the value of x in f(x)

f(x) = 3x³-kn²+21x-10

$f( \frac{2}{3} ) = 3( \frac{2}{3} )³ - k {( \frac{2}{3} )}^{2} + 21( \frac{2}{3} ) - 10$

$= \frac{8}{9} - \frac{4k}{9} + 14 - 10$

$= \frac{8}{9} - \frac{4k}{9} + 4$

$= \frac{8 - 4k + 3b}{9}$

$= \frac{44 - 4k}{9}$

remainder is 0

$\frac{44 - 4k}{9} = 0$

$⟹ {44 - 4k} = 0$

$⟹k = 11$