What are the solutions to the equation a^2x^2+a(b-c)x-bc=0 ?

The solutions to the equation a^2x^2+a(b-c)x-bc=0 are x= c/a ,x=-b/a ;\quad a\ne 0

Find the zeros of a^2x^2+a(b-c)x-bc=0

The zeros of a^2x^2+a(b-c)x-bc=0 are x= c/a ,x=-b/a ;\quad a\ne 0

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a^{2} x^{2} + a (b - c) x - b c = 0

x = \frac{c}{a}, x = - \frac{b}{a}; a \neq = 0

Solution steps

a^{2} x^{2} + a (b - c) x - b c = 0

Expand

a^{2} x^{2} + a (b - c) x - b c : a^{2} x^{2} + ab x - a c x - b c

a^{2} x^{2} + ab x - a c x - b c = 0

Write in the standard form

a x^{2} + b x + c = 0

a^{2} x^{2} + (ab - a c) x - b c = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( ab - a c ) \pm ( ab - a c ) ^{2} - 4 a ^{2} ( - b c )}{2 a ^{2}}

Simplify

(ab - a c)^{2} - 4 a^{2} (- b c) : a (b + c)

x_{1, 2} = \frac{- ( ab - a c ) \pm a ( b + c )}{2 a ^{2}}; a \neq = 0

Separate the solutions

x_{1} = \frac{- ( ab - a c ) + a ( b + c )}{2 a ^{2}}, x_{2} = \frac{- ( ab - a c ) - a ( b + c )}{2 a ^{2}}

x = \frac{- ( ab - a c ) + a ( b + c )}{2 a ^{2}} : \frac{c}{a}

x = \frac{- ( ab - a c ) - a ( b + c )}{2 a ^{2}} : - \frac{b}{a}

The solutions to the quadratic equation are:

x = \frac{c}{a}, x = - \frac{b}{a}; a \neq = 0

0 = 210 + 205.06 t - 4.9 t^{2}

- 60 = 2 (h + 7)^{2} + 4

2 x^{2} - 8 = 10

x^{2} + 6 x = 80

(x - 1)^{2} + (0 + 1)^{2} = 9

What are the solutions to the equation a^2x^2+a(b-c)x-bc=0 ?
The solutions to the equation a^2x^2+a(b-c)x-bc=0 are x= c/a ,x=-b/a ;\quad a\ne 0
Find the zeros of a^2x^2+a(b-c)x-bc=0
The zeros of a^2x^2+a(b-c)x-bc=0 are x= c/a ,x=-b/a ;\quad a\ne 0