Question

verify that-1 is zeros of a polynomial f(x)=x³+x²+x+1 also find the value of f(0)+f(1)-f(2)​

Answer 1

Step-by-step explanation:

f(1)=13−(2×12)+(4×1)+k=1−2+4+k=3+k

Therefore, f(1)=3+k.

Since it is given that x=1 is a zero of the polynomial f(x)=x3−2x2+4x+k, therefore f(1)=0 that is:

3+k=0

⇒k=−3

Hence k=−3.

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Answer 2

Step-by-step explanation:

♦ Given ♦ :-

• f(x) = x³+x²+x+1

♦ To find ♦ :-

• -1 is a zero of f(x)
• The value of f(0)+f(1)-f(2)

♦ Solution ♦ :-

Given polynomial is f(x) = x³+x²+x+1 --------(1)

Put x = -1 in (1) then

=> f(-1) = (-1)³+(-1)²+(-1)+1

=> f(-1) = -1+1-1+1

=> f(-1) = 2-2

=> f(-1) = 0

Therefore, -1 is a zero of f(x).

now,

Put x = 0 in (1) then

f(0) = 0³+0²+0+1

=> f(0) = 0+0+0+1

=> f(0) = 1

Put x = 1 in (1) then

=> f(1) = 1³+1²+1+1

=> f(1) = 1+1+1+1

=> f(1) = 4

put x = 2 in (1) then

=> f(2) = 2³+2²+2+1

=> f(2) = 8+4+2+1

=> f(2) = 15

Now, The value of f(0)+f(1)-f(2)

= 1 + 4 - 15

= 5 - 15

= -10

♦ Answer ♦ :-

The value of f(0)+f(1)-f(2) is -10