Question

Using the quadratic formula, Solve the following

p2x2 + ( p2 - q2)x - q2 = 0.

Answer 1

${p}^{2} {x}^{2} + ( {p}^{2} - {q}^{2} )x - {q}^{2} = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a } \\ x = \frac{ {q}^{2} - {p}^{2} + - \sqrt{ {p}^{4} + {q}^{4} - 2 {p}^{2} {q}^{2} + 4 {p}^{2} {q}^{2} }}{2 {p}^{2} } \\ x = \frac{{q}^{2} - {p}^{2} + - ( {p}^{2} + {q}^{2}) }{2 {p}^{2} } \\ x = \frac{ {q}^{2} }{ {p}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 1$
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