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. -py, qy

Answer 1

The correct option is C

py, qy

$\text{‘-p’ and ‘q’ are the zeroes of the polynomial}{x}^2–bx+c.\text{We know the expresion of roots is}{x}^2-(\alpha +\beta )x+\alpha \beta \Rightarrow b=p+q,\text{and}c=pq\text{Substitute in}{x}^2–bxy+c{y}^2{x}^2–bxy+c{y}^2=x^2–(p+q)xy+pq{y}^2=x^2-(py+qy)x+\left(py\right)\left(qy\right)\therefore \alpha =py\text{and}\beta =qy\text{Thus, the zeroes of the polynomial}{x}^2–bxy+c{y}^2\text{are}py\text{and}qy.$