Solve x^4-5x^24 - ScanMath

Question

Simplify the expression

x^{4} - 20 x^{2}

Evaluate

x^{4} - 5 x^{2} \times 4

Solution

x^{4} - 20 x^{2}

Show Solution

x^{2} (x^{2} - 20)

Evaluate

x^{4} - 5 x^{2} \times 4

Multiply the terms

x^{4} - 20 x^{2}

Rewrite the expression

x^{2} \times x^{2} - x^{2} \times 20

Solution

x^{2} (x^{2} - 20)

Show Solution

x_{1} = - 25, x_{2} = 0, x_{3} = 25

Alternative Form

x_{1} \approx - 4.472136, x_{2} = 0, x_{3} \approx 4.472136

Evaluate

x^{4} - 5 x^{2} \times 4

To find the roots of the expression,set the expression equal to 0

x^{4} - 5 x^{2} \times 4 = 0

Multiply the terms

x^{4} - 20 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 20) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 20 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x^{2} - 20 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 20 = 0

Move the constant to the right-hand side and change its sign

x^{2} = 0 + 20

Removing 0 doesn't change the value,so remove it from the expression

x^{2} = 20

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 20

Simplify the expression

More Steps

Evaluate

20

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

The root of a product is equal to the product of the roots of each factor

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

x = \pm 25

Separate the equation into 2 possible cases

x = 25 x = - 25

x = 0 x = 25 x = - 25

Solution

x_{1} = - 25, x_{2} = 0, x_{3} = 25

Alternative Form

x_{1} \approx - 4.472136, x_{2} = 0, x_{3} \approx 4.472136

Show Solution