Solve (9k^6 8k^4-6k^2)(4k^2-5)

Question

Simplify the expression

288 k^{12} - 360 k^{10} - 24 k^{4} + 30 k^{2}

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6 k^{2} (12 k^{8} - 1) (4 k^{2} - 5)

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k_{1} = - \frac{5}{2}, k_{2} = - \frac{8 1 2 ^{7}}{12}, k_{3} = 0, k_{4} = \frac{8 1 2 ^{7}}{12}, k_{5} = \frac{5}{2}

Alternative Form

k_{1} \approx - 1.118034, k_{2} \approx - 0.732997, k_{3} = 0, k_{4} \approx 0.732997, k_{5} \approx 1.118034

Evaluate

(9 k^{6} \times 8 k^{4} - 6 k^{2}) (4 k^{2} - 5)

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

(9 k^{6} \times 8 k^{4} - 6 k^{2}) (4 k^{2} - 5) = 0

Multiply

More Steps

(72 k^{10} - 6 k^{2}) (4 k^{2} - 5) = 0

Separate the equation into 2 possible cases

72 k^{10} - 6 k^{2} = 0 4 k^{2} - 5 = 0

Solve the equation

More Steps

k = 0 k = \frac{8 1 2 ^{7}}{12} k = - \frac{8 1 2 ^{7}}{12} 4 k^{2} - 5 = 0

Solve the equation

More Steps

k = 0 k = \frac{8 1 2 ^{7}}{12} k = - \frac{8 1 2 ^{7}}{12} k = \frac{5}{2} k = - \frac{5}{2}

Solution

k_{1} = - \frac{5}{2}, k_{2} = - \frac{8 1 2 ^{7}}{12}, k_{3} = 0, k_{4} = \frac{8 1 2 ^{7}}{12}, k_{5} = \frac{5}{2}

Alternative Form

k_{1} \approx - 1.118034, k_{2} \approx - 0.732997, k_{3} = 0, k_{4} \approx 0.732997, k_{5} \approx 1.118034

Show Solution