Question

Solve by using quadratic formula:
p^2x^2+(p^2-q^2)x-q^2=0

Answer 1

Hi ,

p² x² + ( p² - q² ) x - q² = 0 compare

with ax² + bx + c = 0 we get ,

a = p² ,

b = p² - q² ,

c = - q² ,

Discreaminant = b² - 4ac

D = ( p² - q² )² - 4p² ( - q² )

= ( p² - q² )² + 4p²q²

= ( p² + q² )²

√D = ± ( p² + q² )

By quadratic formula ,

x = [ -b ± √D ] / 2a

= [ - ( p² - q² ) ± ( p² + q² ) ] / 2p²

Therefore ,

x = [ -(p²-q²)+(p²+ q²)]/2p²

= ( 2q² ) /2p²

= q²/p²

Or

x = [ -(p²-q²)-(p²+q² )] /2p²

= ( -2p² ) / 2q²

= - p² / q²

I hope this helps you.

: )