Question

solve for x 6^2x^2+(b^2-q^2)x-q^2=0​

Answer 1

Answer:

Given quadratic equation is 

p²x² + ( p² - q² )x - q² = 0

dividing each term with p² ,

p²x² / p² + [ ( p² - q² ) / p² ] x - q² / p² = 0

⇒ x²  + [ 1 - q² / p² ] x - q² / p² = 0

 To find the roots split the middle term

⇒     x² + x - ( q² / p² ) x - q² / p² = 0

⇒  x ( x + 1 ) - ( q² / p² ) ( x + 1) = 0

⇒                ( x+ 1 ) ( x - q² /p² ) = 0

Therefore,

                 x+1 =0  or  x - q² / p² =0

            x= -1 or       x  = q²