What are the solutions to the equation 4x^4-28x^3+61x^2-42x+9=0 ?

The solutions to the equation 4x^4-28x^3+61x^2-42x+9=0 are x=3,x= 1/2

Find the zeros of 4x^4-28x^3+61x^2-42x+9=0

The zeros of 4x^4-28x^3+61x^2-42x+9=0 are x=3,x= 1/2

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4 x^{4} - 28 x^{3} + 61 x^{2} - 42 x + 9 = 0

x = 3, x = \frac{1}{2}

Decimal Notation

x = 3, x = 0.5

Solution steps

4 x^{4} - 28 x^{3} + 61 x^{2} - 42 x + 9 = 0

Factor

4 x^{4} - 28 x^{3} + 61 x^{2} - 42 x + 9 : (x - 3)^{2} (2 x - 1)^{2}

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or 2 x - 1 = 0

Solve

x - 3 = 0 : x = 3

Solve

2 x - 1 = 0 : x = \frac{1}{2}

The solutions are

x = 3, x = \frac{1}{2}

16 x^{4} - 52 x^{2} + 36 = 0

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

x^{5} = 18 x^{3} - 81 x

m^{5} + 5 m^{4} - 2 m^{3} - 10 m^{2} + m + 5 = 0

(x - 1)^{4} - (x - 1)^{2} - 12 = 0

What are the solutions to the equation 4x^4-28x^3+61x^2-42x+9=0 ?
The solutions to the equation 4x^4-28x^3+61x^2-42x+9=0 are x=3,x= 1/2
Find the zeros of 4x^4-28x^3+61x^2-42x+9=0
The zeros of 4x^4-28x^3+61x^2-42x+9=0 are x=3,x= 1/2