Solve 2x^4-3x-5x^2

Question

Factor the expression

x (x + 1) (2 x^{2} - 2 x - 3)

Evaluate

2 x^{4} - 3 x - 5 x^{2}

Evaluate

2 x^{4} - 5 x^{2} - 3 x

Rewrite the expression

x \times 2 x^{3} - x \times 5 x - x \times 3

Factor out x from the expression

x (2 x^{3} - 5 x - 3)

Solution

More Steps

Evaluate

2 x^{3} - 5 x - 3

Calculate

2 x^{3} - 2 x^{2} - 3 x + 2 x^{2} - 2 x - 3

Rewrite the expression

x \times 2 x^{2} - x \times 2 x - x \times 3 + 2 x^{2} - 2 x - 3

Factor out x from the expression

x (2 x^{2} - 2 x - 3) + 2 x^{2} - 2 x - 3

Factor out 2 x^{2} - 2 x - 3 from the expression

(x + 1) (2 x^{2} - 2 x - 3)

x (x + 1) (2 x^{2} - 2 x - 3)

Show Solution

Find the roots

x_{1} = - 1, x_{2} = \frac{1 - 7}{2}, x_{3} = 0, x_{4} = \frac{1 + 7}{2}

Alternative Form

x_{1} = - 1, x_{2} \approx - 0.822876, x_{3} = 0, x_{4} \approx 1.822876

Evaluate

2 x^{4} - 3 x - 5 x^{2}

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

2 x^{4} - 3 x - 5 x^{2} = 0

Factor the expression

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

Separate the equation into 3 possible cases

x = 0 x + 1 = 0 2 x^{2} - 2 x - 3 = 0

Solve the equation

More Steps

Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

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

Solve the equation

More Steps

Evaluate

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

Substitute a= 2,b= - 2 and c= - 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 ( - 3 )}{2 \times 2}

Simplify the expression

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 ( - 3 )}{4}

Simplify the expression

More Steps

Evaluate

(- 2)^{2} - 4 \times 2 (- 3)

Multiply

(- 2)^{2} - (- 24)

Rewrite the expression

2^{2} - (- 24)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2^{2} + 24

Evaluate the power

4 + 24

Add the numbers

28

x = \frac{2 \pm 28}{4}

Simplify the radical expression

More Steps

Evaluate

28

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

4 \times 7

Write the number in exponential form with the base of 2

2^{2} \times 7

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

2^{2} \times 7

Reduce the index of the radical and exponent with 2

27

x = \frac{2 \pm 2 7}{4}

Separate the equation into 2 possible cases

x = \frac{2 + 2 7}{4} x = \frac{2 - 2 7}{4}

Simplify the expression

x = \frac{1 + 7}{2} x = \frac{2 - 2 7}{4}

Simplify the expression

x = \frac{1 + 7}{2} x = \frac{1 - 7}{2}

x = 0 x = - 1 x = \frac{1 + 7}{2} x = \frac{1 - 7}{2}

Solution

x_{1} = - 1, x_{2} = \frac{1 - 7}{2}, x_{3} = 0, x_{4} = \frac{1 + 7}{2}

Alternative Form

x_{1} = - 1, x_{2} \approx - 0.822876, x_{3} = 0, x_{4} \approx 1.822876

Show Solution