If –2 is a zero of the polynomial x2– x – (2+ 2k), then the value of k is ____

2 thoughts on “If –2 is a zero of the polynomial x2– x – (2+ 2k), then the value of k is ____”

1. Step-by-step explanation:

   Given :–

   –2 is a zero of the polynomial x^2– x – (2+ 2k)

   To find :–

   Find the value of k ?

   Solution :–

   Given quadratic polynomial = x^2– x – (2+ 2k)

   Let P(x) = x^2– x – (2+ 2k)

   Given zero of P(x) = -2

   We know that,

   Factor Theorem :-

   P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice versa.

   So, -2 is a zero of P(x) then it satisfies the polynomial

   => P(-2) = 0

   => (-2)^2 -(-2)-(2+2k) = 0

   => 4 + 2 -(2 +2k) = 0

   => 6 – (2+2k) = 0

   => 6 – 2 -2k = 0

   => 4 -2k = 0

   => 4 = 2k

   => 2k = 4

   => k = 4/2

   => k = 2

   Therefore,k = 2

   Answer:–

   The valie of k for the given problem is 2

   Used formulae:–

   Factor Theorem :-

   P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice versa.

   Reply

2. Step-by-step explanation:

   x²– x – (2+ 2k)=0

   =>4+2-2-2k=0

   =>2k=4

   =>k=2

   Reply