Solve 4a^4-5a^21 - ScanMath

Question

Simplify the expression

4 a^{4} - 5 a^{2}

Evaluate

4 a^{4} - 5 a^{2} \times 1

Solution

4 a^{4} - 5 a^{2}

Show Solution

a^{2} (4 a^{2} - 5)

Evaluate

4 a^{4} - 5 a^{2} \times 1

Multiply the terms

4 a^{4} - 5 a^{2}

Rewrite the expression

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

Solution

a^{2} (4 a^{2} - 5)

Show Solution

a_{1} = - \frac{5}{2}, a_{2} = 0, a_{3} = \frac{5}{2}

Alternative Form

a_{1} \approx - 1.118034, a_{2} = 0, a_{3} \approx 1.118034

Evaluate

4 a^{4} - 5 a^{2} \times 1

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

4 a^{4} - 5 a^{2} \times 1 = 0

Multiply the terms

4 a^{4} - 5 a^{2} = 0

Factor the expression

a^{2} (4 a^{2} - 5) = 0

Separate the equation into 2 possible cases

a^{2} = 0 4 a^{2} - 5 = 0

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

a = 0 4 a^{2} - 5 = 0

Solve the equation

More Steps

Evaluate

4 a^{2} - 5 = 0

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

4 a^{2} = 0 + 5

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

4 a^{2} = 5

Divide both sides

\frac{4 a ^{2}}{4} = \frac{5}{4}

Divide the numbers

a^{2} = \frac{5}{4}

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

a = \pm \frac{5}{4}

Simplify the expression

More Steps

Evaluate

\frac{5}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{5}{4}

Simplify the radical expression

\frac{5}{2}

a = \pm \frac{5}{2}

Separate the equation into 2 possible cases

a = \frac{5}{2} a = - \frac{5}{2}

a = 0 a = \frac{5}{2} a = - \frac{5}{2}

Solution

a_{1} = - \frac{5}{2}, a_{2} = 0, a_{3} = \frac{5}{2}

Alternative Form

a_{1} \approx - 1.118034, a_{2} = 0, a_{3} \approx 1.118034

Show Solution