Question

If‘-p’ and ‘q’ are the zeroes of the polynomial
$x^2–bx+c$, then the zeroes of the polynomial $x^2–bxy+c{y}^2$ are ________.

• A. $-py\&qy$
• B. $py\&-qy$
• C. $py\&qy$
• D. $-py\&-qy$

Answer 1

The correct option is A

$-py\&qy$

Given ‘-p’ and ‘q’ are the zeroes of the polynomial $x^2–bx+c$.
$⟹x^2–bx+c=(x+p)(x-q)$.
$⟹x^2-bx+c=x^2+px-qx-pq$
$⟹-b=(p-q),\text{and}c=-pq$
$x^2–bxy+c{y}^2=x^2+(p-q)xy-pq{y}^2$
$=x^2+(py-qy)x-\left(py\right)\left(qy\right)$
$=(x+py)(x-qy)$

Thus, the zeroes of the polynomial $x^2–bxy+c{y}^2$ are $-py$ and $qy$.