If –2 is a zero of the polynomial x2– x – (2+ 2k), then the value of k is ____
Answers
Step-by-step explanation:
x²– x – (2+ 2k)=0
=>4+2-2-2k=0
=>2k=4
=>k=2
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.