Solve a^2-13a^4 - ScanMath

Question

Factor the expression

Factor

a^{2} (1 - 13 a^{2})

Evaluate

a^{2} - 13 a^{4}

Rewrite the expression

a^{2} - a^{2} \times 13 a^{2}

Solution

a^{2} (1 - 13 a^{2})

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Find the roots of the algebra expression

a_{1} = - \frac{13}{13}, a_{2} = 0, a_{3} = \frac{13}{13}

Alternative Form

a_{1} \approx - 0.27735, a_{2} = 0, a_{3} \approx 0.27735

Evaluate

a^{2} - 13 a^{4}

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

a^{2} - 13 a^{4} = 0

Factor the expression

a^{2} (1 - 13 a^{2}) = 0

Separate the equation into 2 possible cases

a^{2} = 0 1 - 13 a^{2} = 0

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

a = 0 1 - 13 a^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 13 a^{2} = 0

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

- 13 a^{2} = 0 - 1

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

- 13 a^{2} = - 1

Change the signs on both sides of the equation

13 a^{2} = 1

Divide both sides

\frac{13 a ^{2}}{13} = \frac{1}{13}

Divide the numbers

a^{2} = \frac{1}{13}

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

a = \pm \frac{1}{13}

Simplify the expression

More Steps

Evaluate

\frac{1}{13}

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

\frac{1}{13}

Simplify the radical expression

\frac{1}{13}

Multiply by the Conjugate

\frac{13}{13 \times 13}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{13}{13}

a = \pm \frac{13}{13}

Separate the equation into 2 possible cases

a = \frac{13}{13} a = - \frac{13}{13}

a = 0 a = \frac{13}{13} a = - \frac{13}{13}

Solution

a_{1} = - \frac{13}{13}, a_{2} = 0, a_{3} = \frac{13}{13}

Alternative Form

a_{1} \approx - 0.27735, a_{2} = 0, a_{3} \approx 0.27735

Show Solution