Question

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

• A. -py,qy
• B. py,-qy
• C. py,qy
• D. None of these

Answer 1

The correct option is A

-py,qy

‘-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 $qy$.