End-of-chapter review exercise 1: check 1
Difficulty: ★★☆Maths4U Original · Short practice
The roots of \(x^{3} - 39 x^{2} + 506 x - 2184=0\) 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.
End-of-chapter review exercise 1: review variant 1
Difficulty: ★★☆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.
End-of-chapter review exercise 1: check 2
Difficulty: ★★☆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 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.
End-of-chapter review exercise 1: review variant 2
Difficulty: ★★☆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.
End-of-chapter review exercise 1: check 3
Difficulty: ★★☆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 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.
End-of-chapter review exercise 1: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
The roots of \(x^{4} - 66 x^{3} + 1631 x^{2} - 17886 x + 73440=0\) 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.
End-of-chapter review exercise 1: check 4
Difficulty: ★★☆Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 49 x^{2} + 798 x - 4320=0\). The transformed roots are \(4\alpha+15,4\beta+15,4\gamma+15\). Write their monic equation as \(y^3+Ay^2+By+C=0\).
Find the sum of the squares of the transformed roots.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 1: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 52 x^{2} + 899 x - 5168=0\). The transformed roots are \(2\alpha+16,2\beta+16,2\gamma+16\). Write their monic equation as \(y^3+Ay^2+By+C=0\).
Find the sum of the squares of the transformed roots.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.