Maths4U Original · Short practice

The roots of \(x^{3} - 42 x^{2} + 587 x - 2730=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). 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.

Maths4U Original · Short practice

The roots of \(x^{3} - 45 x^{2} + 674 x - 3360=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). 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.

Maths4U Original · Short practice

The roots of \(x^{3} - 45 x^{2} + 674 x - 3360=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). 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.

Maths4U Original · Short practice

The roots of \(x^{3} - 48 x^{2} + 767 x - 4080=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). 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.

Maths4U Original · Short practice

The roots of \(x^{3} - 48 x^{2} + 767 x - 4080=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). 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.

Maths4U Original · Short practice

The roots of \(x^{3} - 51 x^{2} + 866 x - 4896=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). 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.

Maths4U Original · Short practice

The roots of \(x^{3} - 51 x^{2} + 866 x - 4896=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). 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.

Maths4U Original · Short practice

The roots of \(x^{3} - 54 x^{2} + 971 x - 5814=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). 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.