Question

find the quadratic polynomial whose sum of and product of zeros are 1 upon 3 and minus 1 upon 3​

Answer 1

Polynomial f(x)= x-x/3+1/3= 3x-x+1

Answer 2

Answer:

let the zeroes be α & β

given :-

α + β = 1/3

αβ = -1/3

formula to form a quadratic polynomial is

$k[x^{2} - (\alpha + \beta ) + \alpha \beta ]$

k[$k[x^{2} - \frac{1}{3} x + (-\frac{1}{3} )]$

$k[x^{2} -\frac{1}{3} x -\frac{1}{3}]$

Ans : $\frac{k}{3}[3x^{2} -x +1]$      {by taking l.c.m.}

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