Question

if x+2 is a factor of 2x^4+kx find k

Answer 1

The Given equation is, 2x^4 + kx

If, x + 2 is factory then :

➝ x + 2 = 0

➝ x = -2

Put value of x in above equation :

➝ 2x^4 + kx = 0

➝ 2(-2)^4 + k(-2) = 0

➝ 2*16 - 2k = 0

➝ 32 - 2k = 0

➝ -2k = -32

➝ k = 32/2

➝ k = 16

Answer 2

GIVEN :-

• x + 2 is a factor of p(x) = 2x⁴ + kx.

TO FIND :-

• The value of k.

SOLUTION :-

Let,

$: \implies \displaystyle \sf \: x \: + 2 = 0$

$: \implies \underline{ \boxed{ \displaystyle \sf \: x \: = - 2}}$

_________________…

$\\ \dashrightarrow \displaystyle \sf \:p( x )\: = 2x ^{4} + kx = 0$

$\dashrightarrow \displaystyle \sf \:p( - 2) = 2 \times ( - 2) ^{4} + k \times ( - 2) = 0$

$\dashrightarrow \displaystyle \sf \:2 \times 16 + ( - 2k) = 0$

$\dashrightarrow \displaystyle \sf \:32 - 2k = 0$

$\dashrightarrow \displaystyle \sf \: - 2k = 0 - 32$

$\dashrightarrow \displaystyle \sf \: - 2k \: = - 32$

$\dashrightarrow \displaystyle \sf \:2k \: = 32$

$\dashrightarrow \underline{ \boxed{\displaystyle \sf \: \bold{k = 16}}}$