Question

What is the polynomial of the smallest degree with integer coefficients and with zero's 3,1+i,-1​

Answer 1

Answer:

Correct Question:-

Find a Quadratic Polynomial whose sum & product of zeroes are \sf\sqrt{2}

2

and 3 respectively.

AnswEr:-

Polynomial is \sf\; x^2 -\sqrt{2} + 3x

2

−

2

+3

Given:-

Sum of Zeroes = \sf\sqrt{2}

2

Product of zeroes = 3

By using Formula :-

:\implies\large\boxed{\sf{\red {x^2 - (\alpha\;+\;\beta) + (\alpha\;\beta)}}}:⟹

x

2

−(α+β)+(αβ)

\rule{150}2

Sum of Zeroes = \sf\;(\alpha \; + \; \beta)(α+β)

And, Product of zeroes = \sf\; (\alpha\; \beta)(αβ)

Sum of Zeroes = \sf\sqrt{2}

2

Product of zeroes = 3

:\implies\sf\; x^2 - \sqrt{2} + 3:⟹x

2

−

2

+3

:\implies\large\boxed{\sf{\blue{x^2 - \sqrt{2} + 3}}}:⟹

x

2

−

2

+3

\rule{1