What are the solutions to the equation 4x^3+16x^2+x+4=0 ?

The solutions to the equation 4x^3+16x^2+x+4=0 are x=-4,x= 1/2 i,x=-1/2 i

Find the zeros of 4x^3+16x^2+x+4=0

The zeros of 4x^3+16x^2+x+4=0 are x=-4,x= 1/2 i,x=-1/2 i

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4 x^{3} + 16 x^{2} + x + 4 = 0

x = - 4, x = \frac{1}{2} i, x = - \frac{1}{2} i

Solution steps

4 x^{3} + 16 x^{2} + x + 4 = 0

Factor

4 x^{3} + 16 x^{2} + x + 4 : (x + 4) (4 x^{2} + 1)

(x + 4) (4 x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 4 = 0 or 4 x^{2} + 1 = 0

Solve

x + 4 = 0 : x = - 4

Solve

4 x^{2} + 1 = 0 : x = \frac{1}{2} i, x = - \frac{1}{2} i

The solutions are

x = - 4, x = \frac{1}{2} i, x = - \frac{1}{2} i

x^{3} + 5 x^{2} + 7 x + 3 = 0

r^{8} - 17 r^{4} + 16 = 0

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

x^{10} - 1 = 0

y^{4} - 20 y^{2} + 64 = 0

What are the solutions to the equation 4x^3+16x^2+x+4=0 ?
The solutions to the equation 4x^3+16x^2+x+4=0 are x=-4,x= 1/2 i,x=-1/2 i
Find the zeros of 4x^3+16x^2+x+4=0
The zeros of 4x^3+16x^2+x+4=0 are x=-4,x= 1/2 i,x=-1/2 i