Question

If (x+1) is a factor of x²+kx+2 .What is the numerical value of k?

Answer 1

AnsweR :-

• K = 3

GiveN :-

• $\sf \: (x + 1) \: is \: a \: factor \: of \: {x}^{2} + kx + 2$

To FinD :-

• The numerical value of k

SolutioN :-

$\sf \: x + 1 = 0 \\ \\ \sf \: x = - 1$

Putting x = -1 in the polynomial -

$\sf {x}^{2} + kx + 2 = 0 \\ \\ \sf \: ( { - 1)}^{2} + k( - 1) + 2 = 0 \\ \\ \sf \: 1 - k + 2 = 0 \\ \\ \sf \: - k + 3 = 0 \\ \\ \sf \boxed{ \sf \huge \: k = 3}$

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So the value of k is 3.