Question

‘-p’ and ‘q’ are the zeroes of equation $x^2–bx+c=0$. The zeroes of the equation $x^2–bxy+c{y}^2$ = 0 are

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

Answer 1

The correct option is A

-py,qy

The equation having factors (x + p) and (x – q) is simply the product of (x + p) and (x – q) which is equal to $x^2$ + (p – q)x – pq. By comparing the coefficients of $x^2$ + (p – q) x – pq and $x^2$ – bx + c, we obtain b = -(p – q) and c = -pq. Simply put the values of ‘b’ and ‘c’ in the equation $x^2$ – bxy + c$y^2$ and solve for x. Upon solving we get $x^2$ + ( p – q)xy – pq$y^2$ = ( x + py) ( x – qy ). The zeroes are -py and qy.