Substitutions: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 37 x^{2} + 454 x - 1848=0\). The transformed roots are \(3\alpha+11,3\beta+11,3\gamma+11\). Write their monic equation as \(y^3+Ay^2+By+C=0\).
Find A.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitutions: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 40 x^{2} + 531 x - 2340=0\). The transformed roots are \(4\alpha+12,4\beta+12,4\gamma+12\). Write their monic equation as \(y^3+Ay^2+By+C=0\).
Find A.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitutions: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 40 x^{2} + 531 x - 2340=0\). The transformed roots are \(4\alpha+12,4\beta+12,4\gamma+12\). Write their monic equation as \(y^3+Ay^2+By+C=0\).
Find B.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitutions: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 43 x^{2} + 614 x - 2912=0\). The transformed roots are \(2\alpha+13,2\beta+13,2\gamma+13\). Write their monic equation as \(y^3+Ay^2+By+C=0\).
Find B.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitutions: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 43 x^{2} + 614 x - 2912=0\). The transformed roots are \(2\alpha+13,2\beta+13,2\gamma+13\). Write their monic equation as \(y^3+Ay^2+By+C=0\).
Find C.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitutions: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 46 x^{2} + 703 x - 3570=0\). The transformed roots are \(3\alpha+14,3\beta+14,3\gamma+14\). Write their monic equation as \(y^3+Ay^2+By+C=0\).
Find C.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitutions: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The roots α,β,γ satisfy \(x^{3} - 46 x^{2} + 703 x - 3570=0\). The transformed roots are \(3\alpha+14,3\beta+14,3\gamma+14\). 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.
Substitutions: review variant 4
Difficulty: ★★☆Info
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.