Substitutions · 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

Transformed polynomial equations — objective 1

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.

Fresh review variant

Transformed polynomial equations — objective 1

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.

Method

Transformed polynomial equations — objective 2

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.

Fresh review variant

Transformed polynomial equations — objective 2

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.

Apply

Transformed polynomial equations — objective 3

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.

Fresh review variant

Transformed polynomial equations — objective 3

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.

Check understanding

Transformed polynomial equations — objective 4

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.

Fresh review variant

Transformed polynomial equations — objective 4

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.

Try written exam-style problems →