Question

Solve by using quadratic formula:

$6. \: p {}^{2} x {}^{2} + (p {}^{2} - q {}^{2} )x - q {}^{2} = 0$

Ans:
$\frac{q {}^{2} }{p {}^{2} }$
, -1

Standard:- 10

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Answer 1

The answer is explained in the attachment.



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Answer 2

Given,

Quadratic equation = p²x² + ( p² - q² )x -q² = 0

Here,

Coefficient of x²( a ) = p²

Coefficient of x ( b ) = ( p² - q² )

Constant term ( c ) = - q²

Using Quadratic formula ,

⇒ x = ( -b ± √D ) / 2a

Where, D is discriminat that is equal to ( b² - 4ac ).

⇒ D = b² - 4ac

⇒ D = ( p² - q² )² - 4p²( -q² )

⇒ D = ( p² )² + ( q² )² - 2p²q² + 4p²q²

⇒ D = p⁴ + q⁴ + 2p²q²

Squaring root both sides,

⇒ √D = √( p⁴ + q⁴ + 2 × p² × q² )

⇒ √D = √( p² + q² )²

•°• √D = ( p² + q² )

Now,

⇒ x = ( -b ± √D ) / 2a

When,

⇒ x = ( -b + √D ) / 2a

⇒ x = [ -( p² - q² ) + p² + q² ] / 2p²

⇒ x = [ -p² + q² + p² +q² ] / 2p²

⇒x = ( 2q² )/( 2p² )

•°• x = q²/p²

When,

⇒ x = [ -b - √D ] / 2a

⇒ x = [ -( p² - q² ) - ( p² + q² ) ] / 2( p² )

⇒ x = [ -p² + q² - p² - q² ] / 2p²

⇒ x = ( -2p² ) / 2p²

•°• x = -1

Hence , x = ( p²/q² ) or ( -1 ).