Pierwiastkiem wielomianu W nazywamy każda liczbę rzeczywistą a, dla której W(a)=0.

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$\text{a)}$  

$W\left(-1\right)={\left(-1\right)}^4+{\left(-1\right)}^3-7\cdot {\left(-1\right)}^2-\left(-1\right)+6=1-1-7+1+6=0$  

$W\left(2\right)=2^4+2^3-7\cdot 2^2-2+6=16+8-7\cdot 4-2+6=24-28+4=0$  

$W\left(3\right)=3^4+3^3-7\cdot 3^2-3+6=81+27-7\cdot 9+3=81+27-72+3=39\ne 0$  

$W\left(4\right)=4^4+4^3-7\cdot 4^2-4+6=256+64-7\cdot 16+2=320-112+2=210\ne 0$  

Pierwiastkami wielomianu W są liczby: -1, 2.

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$\text{b)}$  

$W\left(-1\right)={\left(-1\right)}^3+{\left(-1\right)}^2+\left(-1\right)+1=-1+1-1+1=0$  

$W\left(2\right)=2^3+2^2+2+1=8+4+2+1=15\ne 0$  

$W\left(3\right)=3^3+3^2+3+1=27+9+3+1=40\ne 0$  

$W\left(4\right)=4^3+4^2+4+1=64+16+4+1=85\ne 0$  

Pierwiastkiem wielomianu W jest liczba -1.

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$\text{c)}$  

$W\left(-1\right)=\left(-1+1\right)\left[{\left(-1\right)}^2-5\cdot \left(-1\right)+6\right]=0\cdot \left(1+5+6\right)=0$  

$W\left(2\right)=\left(2+1\right)\left(2^2-5\cdot 2+6\right)=3\cdot \left(4-10+6\right)=3\cdot 0=0$  

$W\left(3\right)=\left(3+1\right)\left(3^2-5\cdot 3+6\right)=4\cdot \left(9-15+6\right)=4\cdot 0=0$  

$W\left(4\right)=\left(4+1\right)\left(4^2-5\cdot 4+6\right)=5\cdot \left(16-20+6\right)=5\cdot 2=10\ne 0$  

Pierwiastkami wielomianu W są liczby: -1, 2, 3.

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$\text{d)}$  

$W\left(-1\right)={\left(-1-4\right)}^2\left(-1+1\right)\left(-1-3\right)\left(-1-2\right)={\left(-5\right)}^2\cdot 0\cdot \left(-4\right)\cdot \left(-3\right)=0$  

$W\left(2\right)={\left(2-4\right)}^2\left(2+1\right)\left(2-3\right)\left(2-2\right)={\left(-2\right)}^2\cdot 3\cdot \left(-1\right)\cdot 0=0$  

$W\left(3\right)={\left(3-4\right)}^2\left(3+1\right)\left(3-3\right)\left(3-2\right)={\left(-1\right)}^2\cdot 4\cdot 0\cdot 1=0$  

$W\left(4\right)={\left(4-4\right)}^2\left(4+1\right)\left(4-3\right)\left(4-2\right)=0\cdot 5\cdot 1\cdot 2=0$  

Pierwiastkami wielomianu W są liczby: -1, 2, 3, 4.