Question

Find the value of K if p(x)=4x^4+7x^3+8x^2+9kx-15 and g(x)=(x+3).Given gx is the factor of px​

Answer 1

Answer:

put x + 3 = 0

so x = - 3

now x + 3 is a factor of p(x)

therefore p(- 3) = 0

$4 {( - 3)}^{4} + 7 {( - 3)}^{3} + 8 {( - 3)}^{2} + 9k( - 3) - 15 = 0 \\ 324 - 189 + 72 - 27k - 15 = 0 \\ 27k \: = 192 \\ k = \frac{64}{9}$

Answer 2

since GX is the factor of PX

x = -3 put in equation PX we get

0 = 4(81 )+7(-27) +8(9) +9(-3)k - 15

0 = 324 - 189 + 72 - 27k - 15

0 = 192 - 27k

27k = 192 so, k = 192/27 = 64/9

k = 64/9