Question

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​

Answer 1

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.