Question

find the quadratic polynomial whose sum and product of the zeros are root 2 and 1 by 3​

Answer 1

Here given roots 2 and 1/3
Sum =2+1/3=7/3
product=2×1/3=2/3
polynomial is
$x {}^{2} - \frac{7x}{3} + \frac{2}{3} \\ 3x {}^{2} - 7x + 2$

Answer 2

let alpha and beta be the roots of quadratic eqn

alpha=2,beta=1/3

therefore,

quadratic eqn is=x^2-(alpha+beta)x+alpha.beta

=x^2-(2+1/3)x+2*1/3

=x^2-(6+1/3)x+2/3

=x^2-7/3x+2/3

(* by 3)

the quadratic eqn is 3x^2-7x+2=0