Question

check if 1 and 3 are the zeros of the polynomial
$x ^{3} - 6x ^{2} + 11x - 6$
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Answer 1

$\huge\mathfrak{\underline{\underline{Answer:-}}}$

$\sf p(x) x{}^{3}-6x{}^{2}+11x-6$

$\implies\sf p(1)=(1){}^{3}-6(1){}^{2}+11(1)-6$

$\implies\sf p(1)=1-6+11-6$

$\implies\sf p(1)= 12-12$

$\implies\sf p(1)=0$

$\sf 1\: is\: the\: root\: of \: x{}^{3}-6x{}^{2}+11x-6$

$\sf p(x) x{}^{3}-6x{}^{2}+11x-6$

$\implies\sf p(3)=(3){}^{3}-6(3){}^{2}+11(3)-6$

$\implies\sf p(3)=27-54+33-6$

$\implies\sf p(3)=50-60$

$\implies\sf p(3)=-10$

$\sf 3\: is\: not\: the\: root \:of \:x{}^{3}-6x{}^{2}+11x-6$

Answer 2

$\huge\bold{\underline{\underline{Answer:-}}}$

$\rm p(x) x{}^{3}-6x{}^{2}+11x-6$

$\implies\rm p(1)=(1){}^{3}-6(1){}^{2}+11(1)-6$

$\implies\rm p(1)=1-6+11-6$

$\implies\rm p(1)= -5+5$

$\implies\rm p(1)=0$

$\sf 1\: is\: the\: root\: of \: x{}^{3}-6x{}^{2}+11x-6$

$\sf p(x) x{}^{3}-6x{}^{2}+11x-6$

$\implies\rm p(3)=(3){}^{3}-6(3){}^{2}+11(3)-6$

$\implies\rm p(3)=27-54+33-6$

$\implies\rm p(3)=-37+27$

$\implies\rm p(3)=-10$

$\sf 3\: is\: not\: the\: root \:of \:x{}^{3}-6x{}^{2}+11x-6$