What are the solutions to the equation solvefor x,px^2-p(p+3)x+2p(p+1)=0 ?

The solutions to the equation solvefor x,px^2-p(p+3)x+2p(p+1)=0 are x=p+1,x=2;\quad p\ne 0

Find the zeros of solvefor x,px^2-p(p+3)x+2p(p+1)=0

The zeros of solvefor x,px^2-p(p+3)x+2p(p+1)=0 are x=p+1,x=2;\quad p\ne 0

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solve for

x, p x^{2} - p (p + 3) x + 2 p (p + 1) = 0

x = p + 1, x = 2; p \neq = 0

Solution steps

p x^{2} - p (p + 3) x + 2 p (p + 1) = 0

Expand

p x^{2} - p (p + 3) x + 2 p (p + 1) : x^{2} p - x p^{2} - 3 x p + 2 p^{2} + 2 p

x^{2} p - x p^{2} - 3 x p + 2 p^{2} + 2 p = 0

Write in the standard form

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

p x^{2} - (p^{2} + 3 p) x + 2 p^{2} + 2 p = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - p ^{2} - 3 p ) \pm ( - p ^{2} - 3 p ) ^{2} - 4 p ( 2 p ^{2} + 2 p )}{2 p}

Simplify

(- p^{2} - 3 p)^{2} - 4 p (2 p^{2} + 2 p) : p (p - 1)

x_{1, 2} = \frac{- ( - p ^{2} - 3 p ) \pm p ( p - 1 )}{2 p}; p \neq = 0

Separate the solutions

x_{1} = \frac{- ( - p ^{2} - 3 p ) + p ( p - 1 )}{2 p}, x_{2} = \frac{- ( - p ^{2} - 3 p ) - p ( p - 1 )}{2 p}

x = \frac{- ( - p ^{2} - 3 p ) + p ( p - 1 )}{2 p} : p + 1

x = \frac{- ( - p ^{2} - 3 p ) - p ( p - 1 )}{2 p} : 2

The solutions to the quadratic equation are:

x = p + 1, x = 2; p \neq = 0

x, y = x^{2} + 4 x + 9

x, h = - \frac{x}{2} (x - r) + 2

a x^{2} = 2 x + 6

64 + b^{2} = 289

x^{2} = 72 + 363

What are the solutions to the equation solvefor x,px^2-p(p+3)x+2p(p+1)=0 ?
The solutions to the equation solvefor x,px^2-p(p+3)x+2p(p+1)=0 are x=p+1,x=2;\quad p\ne 0
Find the zeros of solvefor x,px^2-p(p+3)x+2p(p+1)=0
The zeros of solvefor x,px^2-p(p+3)x+2p(p+1)=0 are x=p+1,x=2;\quad p\ne 0