Question

If $\alpha$ and $\beta$ are the two zeroes of a polynomial $x^2+6x+a$ then form a polynomial whose zeroes are $-\alpha$ and $-\beta$

Answer 1

If $\alpha ,\beta$ are zeros of

$x^2+6x+a=0$ -------- (1)

then they satisfy the equation as

$x^2-(\alpha +\beta )x+\alpha \beta =0$ where

$\alpha +\beta =6$ & $\alpha \beta =a$

now $\alpha \to -\alpha \leftarrow \beta \to -\beta$ then

$x^2+(\alpha +\beta )x+\alpha \beta =0$

Putting values we get

$x^2-6x+a=0$-------- (2)

equation is polynomial whose zeros aee $-\alpha ,-\beta$