find the value of k l, if x-1 is a factor of p(x) in each of the following cases: p(x)=x^2+x+k
Answers
Given,
p(x) = x² + x + k
g(x) = x - 1
g(x) is a factor of p(x), also g(x) = x - 1
∴ p(1) = 0 [ Factor theorem ]
⇒ p(1) = 0
⇒ (1)² + (1) + k = 0
⇒ 1 + 1 + k = 0
⇒ k = -2
Hence, Value of k is -2.
Verification :-
Put x = 1 in p(x) , It must satisfy the polynomial p(x)
⇒ (1)² + (1) + (-2) = 0
⇒ 1 + 1 - 2 = 0
⇒ 0 = 0
Hence, Verified.
Some Information :-
☛ Given two polynomials p(x) & g(x) if some polynomial q(x) completely divides g(x) then according to the Factor theorem, It would also divide p(x) leaving remainder 0.
☛ A quadratic polynomial can be solved using the quadratic formula or splitting the middle term or completing square method.
A quadratic polynomial is a polynomial of degree 2.
Degree of a polynomial is the highest power of the variable.