Quartics · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Quartic roots and power sums — objective 1

Maths4U Original · Short practice

The roots of \(x^{4} - 46 x^{3} + 791 x^{2} - 6026 x + 17160=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3,\alpha_4\). Use symmetric sums rather than numerical root finding.

Find the sum of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Quartic roots and power sums — objective 1

Maths4U Original · Short practice

The roots of \(x^{4} - 50 x^{3} + 935 x^{2} - 7750 x + 24024=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3,\alpha_4\). Use symmetric sums rather than numerical root finding.

Find the sum of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Quartic roots and power sums — objective 2

Maths4U Original · Short practice

The roots of \(x^{4} - 50 x^{3} + 935 x^{2} - 7750 x + 24024=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3,\alpha_4\). Use symmetric sums rather than numerical root finding.

Find the sum of the squares of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Quartic roots and power sums — objective 2

Maths4U Original · Short practice

The roots of \(x^{4} - 54 x^{3} + 1091 x^{2} - 9774 x + 32760=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3,\alpha_4\). Use symmetric sums rather than numerical root finding.

Find the sum of the squares of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Quartic roots and power sums — objective 3

Maths4U Original · Short practice

The roots of \(x^{4} - 54 x^{3} + 1091 x^{2} - 9774 x + 32760=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3,\alpha_4\). Use symmetric sums rather than numerical root finding.

Find the sum of the reciprocals of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Quartic roots and power sums — objective 3

Maths4U Original · Short practice

The roots of \(x^{4} - 58 x^{3} + 1259 x^{2} - 12122 x + 43680=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3,\alpha_4\). Use symmetric sums rather than numerical root finding.

Find the sum of the reciprocals of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Quartic roots and power sums — objective 4

Maths4U Original · Short practice

The roots of \(x^{4} - 58 x^{3} + 1259 x^{2} - 12122 x + 43680=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3,\alpha_4\). Use symmetric sums rather than numerical root finding.

Find the sum of the cubes of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Quartic roots and power sums — objective 4

Maths4U Original · Short practice

The roots of \(x^{4} - 62 x^{3} + 1439 x^{2} - 14818 x + 57120=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3,\alpha_4\). Use symmetric sums rather than numerical root finding.

Find the sum of the cubes of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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