Find a cubic polynomial whose zeros are $a, b, c$ such that $a + b + c = 4, a b + b c + c a = 1$ and $a b c = - 6$ .

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Solution

A cubic polynomial whose zeros are $a, b, c$ is given by
$p (x) = x^{3} - (a + b + c) x^{2} + (a b + b c + c a) x - a b c$
Thus, the cubic polynomial is
$p (x) = x^{3} - 4 x^{2} + x + 6$

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Find a cubic polynomial whose zeros are a,b,c such that a+b+c=4,ab+bc+ca=1 and abc=−6.

A cubic polynomial whose zeros are a,b,c is given byp(x)=x3−(a+b+c)x2+(ab+bc+ca)x−abcThus, the cubic polynomial isp(x)=x3−4x2+x+6

Find a cubic polynomial whose zeros are $a, b, c$ such that $a + b + c = 4, a b + b c + c a = 1$ and $a b c = - 6$ .

A cubic polynomial whose zeros are $a, b, c$ is given by
$p (x) = x^{3} - (a + b + c) x^{2} + (a b + b c + c a) x - a b c$
Thus, the cubic polynomial is
$p (x) = x^{3} - 4 x^{2} + x + 6$