What are the solutions to the equation solvefor x,p^2x^2+(p^2-q^2)x-q^2=0 ?

The solutions to the equation solvefor x,p^2x^2+(p^2-q^2)x-q^2=0 are x=(q^2)/(p^2),x=-1;\quad p\ne 0

Find the zeros of solvefor x,p^2x^2+(p^2-q^2)x-q^2=0

The zeros of solvefor x,p^2x^2+(p^2-q^2)x-q^2=0 are x=(q^2)/(p^2),x=-1;\quad p\ne 0

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solve for

x, p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0

x = \frac{q ^{2}}{p ^{2}}, x = - 1; p \neq = 0

Solution steps

p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( p ^{2} - q ^{2} ) \pm ( p ^{2} - q ^{2} ) ^{2} - 4 p ^{2} ( - q ^{2} )}{2 p ^{2}}

Simplify

(p^{2} - q^{2})^{2} - 4 p^{2} (- q^{2}) : p^{2} + q^{2}

x_{1, 2} = \frac{- ( p ^{2} - q ^{2} ) \pm ( p ^{2} + q ^{2} )}{2 p ^{2}}; p \neq = 0

Separate the solutions

x_{1} = \frac{- ( p ^{2} - q ^{2} ) + p ^{2} + q ^{2}}{2 p ^{2}}, x_{2} = \frac{- ( p ^{2} - q ^{2} ) - ( p ^{2} + q ^{2} )}{2 p ^{2}}

x = \frac{- ( p ^{2} - q ^{2} ) + p ^{2} + q ^{2}}{2 p ^{2}} : \frac{q ^{2}}{p ^{2}}

x = \frac{- ( p ^{2} - q ^{2} ) - ( p ^{2} + q ^{2} )}{2 p ^{2}} : - 1

The solutions to the quadratic equation are:

x = \frac{q ^{2}}{p ^{2}}, x = - 1; p \neq = 0

25 = 7 + 35 t - 16 t^{2}

14 x^{2} + 17 x - 6 = 0

- 4 x^{2} - 8 x = - 32

4.9 x^{2} + 6.69 x - 2.66 = 0

x^{2} + 40 x - 176 = 0

What are the solutions to the equation solvefor x,p^2x^2+(p^2-q^2)x-q^2=0 ?
The solutions to the equation solvefor x,p^2x^2+(p^2-q^2)x-q^2=0 are x=(q^2)/(p^2),x=-1;\quad p\ne 0
Find the zeros of solvefor x,p^2x^2+(p^2-q^2)x-q^2=0
The zeros of solvefor x,p^2x^2+(p^2-q^2)x-q^2=0 are x=(q^2)/(p^2),x=-1;\quad p\ne 0