What are the solutions to the equation solvefor r,αr^2+r+αr+1=0 ?

The solutions to the equation solvefor r,αr^2+r+αr+1=0 are r=-1/α ,r=-1;\quad α\ne 0

Find the zeros of solvefor r,αr^2+r+αr+1=0

The zeros of solvefor r,αr^2+r+αr+1=0 are r=-1/α ,r=-1;\quad α\ne 0

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solve for

r, α r^{2} + r + α r + 1 = 0

r = - \frac{1}{α}, r = - 1; α \neq = 0

Solution steps

α r^{2} + r + α r + 1 = 0

Write in the standard form

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

α r^{2} + (1 + α) r + 1 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( 1 + α ) \pm ( 1 + α ) ^{2} - 4 α \cdot 1}{2 α}

Simplify

(1 + α)^{2} - 4 α \cdot 1 : α - 1

r_{1, 2} = \frac{- ( 1 + α ) \pm ( α - 1 )}{2 α}; α \neq = 0

Separate the solutions

r_{1} = \frac{- ( 1 + α ) + α - 1}{2 α}, r_{2} = \frac{- ( 1 + α ) - ( α - 1 )}{2 α}

r = \frac{- ( 1 + α ) + α - 1}{2 α} : - \frac{1}{α}

r = \frac{- ( 1 + α ) - ( α - 1 )}{2 α} : - 1

The solutions to the quadratic equation are:

r = - \frac{1}{α}, r = - 1; α \neq = 0

3 x^{2} + 16 = 2 x^{2}

x^{2} + 41 = - 8 x

s^{2} + 2 s + 1

s^{2} + 4 s + 5

3 x + x^{2} = 10

What are the solutions to the equation solvefor r,αr^2+r+αr+1=0 ?
The solutions to the equation solvefor r,αr^2+r+αr+1=0 are r=-1/α ,r=-1;\quad α\ne 0
Find the zeros of solvefor r,αr^2+r+αr+1=0
The zeros of solvefor r,αr^2+r+αr+1=0 are r=-1/α ,r=-1;\quad α\ne 0