Question

if x=2 is a zero of the polynomial f(x)=x4-x3-4x2+kx+10, then find the value of K.

Answer 1

Answer:

k = -1

Step-by-step explanation:

GIVEN

It is given that x = 2 is a zero of the polynomial f(x)

f(x) = x⁴ - x³ - 4x² + kx + 10

CONCEPT OF ZERO OF POLYNOMIAL

Any number 'a' is called a zero of a polynomial f(x) iff (x - a) is a factor of f(x). In other word 'a' is called zero of f(x) iff

f(a) = 0

CALCULATION

x = 2 is a zero of f(x), so

f(2) = 0

or 2⁴ -2³ - 4.2² + k.2 + 10 = 0

or 16 - 8 - 16 + 2k + 10 = 0

or 2k + 2 = 0

or 2k = -2

or k = -1