What are the solutions to the equation p^4-4p+3=0 ?

The solutions to the equation p^4-4p+3=0 are p=-1+sqrt(2)i,p=-1-sqrt(2)i,p=1

Find the zeros of p^4-4p+3=0

The zeros of p^4-4p+3=0 are p=-1+sqrt(2)i,p=-1-sqrt(2)i,p=1

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p^{4} - 4 p + 3 = 0

p = - 1 + 2 i, p = - 1 - 2 i, p = 1

Solution steps

p^{4} - 4 p + 3 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

p^{2} + 2 p + 3 = 0 or p - 1 = 0

Solve

p^{2} + 2 p + 3 = 0 : p = - 1 + 2 i, p = - 1 - 2 i

Solve

p - 1 = 0 : p = 1

The solutions are

p = - 1 + 2 i, p = - 1 - 2 i, p = 1

x^{3} - 6 x^{2} + 9 x - 3 = 0

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

4 x^{3} - 8 x^{2} - 25 x + 50 = 0

4 x^{3} + 12 x^{2} + 9 x = 0

y, 9 x^{5} + 6 y^{3} = 5 x + 10 x^{6}

What are the solutions to the equation p^4-4p+3=0 ?
The solutions to the equation p^4-4p+3=0 are p=-1+sqrt(2)i,p=-1-sqrt(2)i,p=1
Find the zeros of p^4-4p+3=0
The zeros of p^4-4p+3=0 are p=-1+sqrt(2)i,p=-1-sqrt(2)i,p=1