Question

If(3x-2) is a factor of 3x3-kx2+21x-10 find the value of k

Answer 1

Solution :

(3x-2) is a factor of the given polynomial

$\star \sf \: 3x - 2 = 0$

$\rightarrow \sf \: 3x = 0 + 2$

$\rightarrow \sf \: 3x = 2$

$\rightarrow \sf \red{ x = \dfrac{2}{3} }$

$\star \sf \: P(x) = 3 {x}^{3} - k {x}^{2} + 21x - 10$

Putting the value of x = 2/3

$\rightarrow \sf \:P( \dfrac{2}{3} ) = 3(\dfrac{ 2}{3} ) ^{3} - k( \dfrac{2}{3} )^{2} + 21( \dfrac{2}{3} ) - 10$

$\rightarrow \sf 3 \times \dfrac{8}{27} - k \times \dfrac{4}{9} + 21 \times \dfrac{2}{3} - 10$

$\rightarrow \sf \cancel \dfrac{24}{27} - \dfrac{4k}{9} + \cancel\dfrac{42}{3} - 10$

$\rightarrow \sf \dfrac{8}{9} - \dfrac{4k}{9} + 14 - 10$

$\rightarrow \sf \dfrac{8}{9} - \dfrac{4k}{9} +4$

$\rightarrow \sf \dfrac{8 - 4k + 36}{9} = 0$

$\rightarrow \sf \dfrac{44 - 4k }{9} = 0$

$\rightarrow \sf 44 - 4k = 0$

$\rightarrow \sf - 4k = 0 - 44$

$\rightarrow \sf - 4k = - 44$

$\rightarrow \sf \large\boxed { \sf k = 11}$

Hence,The value of k = 11

Answer 2

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