What are the solutions to the equation 4x^4-22x^3+38x^2-44x+60=0 ?

The solutions to the equation 4x^4-22x^3+38x^2-44x+60=0 are x=3,x= 5/2 ,x=sqrt(2)i,x=-sqrt(2)i

Find the zeros of 4x^4-22x^3+38x^2-44x+60=0

The zeros of 4x^4-22x^3+38x^2-44x+60=0 are x=3,x= 5/2 ,x=sqrt(2)i,x=-sqrt(2)i

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4 x^{4} - 22 x^{3} + 38 x^{2} - 44 x + 60 = 0

x = 3, x = \frac{5}{2}, x = 2 i, x = - 2 i

Solution steps

4 x^{4} - 22 x^{3} + 38 x^{2} - 44 x + 60 = 0

Factor

4 x^{4} - 22 x^{3} + 38 x^{2} - 44 x + 60 : 2 (x - 3) (2 x - 5) (x^{2} + 2)

2 (x - 3) (2 x - 5) (x^{2} + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or 2 x - 5 = 0 or x^{2} + 2 = 0

Solve

x - 3 = 0 : x = 3

Solve

2 x - 5 = 0 : x = \frac{5}{2}

Solve

x^{2} + 2 = 0 : x = 2 i, x = - 2 i

The solutions are

x = 3, x = \frac{5}{2}, x = 2 i, x = - 2 i

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

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

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

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

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

What are the solutions to the equation 4x^4-22x^3+38x^2-44x+60=0 ?
The solutions to the equation 4x^4-22x^3+38x^2-44x+60=0 are x=3,x= 5/2 ,x=sqrt(2)i,x=-sqrt(2)i
Find the zeros of 4x^4-22x^3+38x^2-44x+60=0
The zeros of 4x^4-22x^3+38x^2-44x+60=0 are x=3,x= 5/2 ,x=sqrt(2)i,x=-sqrt(2)i