Question

the quadratic polynomial whose zeroes are 5+√3 and 5-√3 is​

Answer 1

Answer:

it is not a 0 of the polynomial and it is also not a quadratic polynomial

Answer 2

Answer:

$\sf{The \ required \ polynomial \ is}$

$\sf{p(x)=x^{2}-10x+22.}$

Given:

$\sf{The \ zeroes \ of \ the \ polynomial \ are}$

$\sf{5+\sqrt3 \ and \ 5-\sqrt3.}$

To find:

$\sf{The \ quadratic \ polynomial.}$

Solution:

$\sf{Let \ \alpha=5+\sqrt3 \ and \ \beta=5-\sqrt3}$

$\sf{\alpha+\beta=(5+\sqrt3)+(5-\sqrt3)}$

$\sf{\therefore{\alpha+\beta=10...(1)}}$

$\sf{\alpha\beta=(5+\sqrt3)(5-\sqrt3)}$

$\sf{\therefore{\alpha\beta=5^{2}-\sqrt3^{2}}}$

$\sf{\therefore{\alpha\beta=25-3}}$

$\sf{\therefore{\alpha\beta=22...(2)}}$

$\sf{Quadratic \ polynomial \ can \ be \ written}$

$\sf{as}$

$\sf{p(x)=x^{2}-(\alpha+\beta)x+\alpha\beta}$

$\sf{from \ (1) \ and \ (2)}$

$\sf{p(x)=x^{2}-10x+22}$

$\sf\purple{\tt{\therefore{The \ required \ polynomial \ is}}}$

$\sf\purple{\tt{p(x)=x^{2}-10x+22.}}$