Linear Transformations of Roots (Edexcel A-Level Further Mathematics): Quizzes

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Linear Transformations of Roots
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What does a linear transformation of roots create?

A new polynomial with related roots

In the general form y=pα+qy = p\alpha + q, what do pp and qq represent?

Constants

What is the first step when transforming roots using y=pα+qy = p\alpha + q?

Express xx in terms of yy

To clear fractions, multiply by what power when the original polynomial has degree nn?

pnp^n

For transformation y=2x+3y = 2x + 3, what is xx expressed in terms of yy?

x=y−32x = \frac{y - 3}{2}

In Example 1, what number is used to multiply through and clear fractions?

8

For transformation y=3x−4y = 3x - 4, what is xx in terms of yy?

x=y+43x = \frac{y + 4}{3}

In Example 2, what value clears fractions (since 33=273^3 = 27)?

27

Which is a common mistake when transforming roots?

Expanding (y−q)n(y - q)^n incorrectly

After rearranging the transformation, what replaces xx in the original polynomial?

y−qp\frac{y - q}{p}

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

Roots of Polynomials

Series

Maclaurin Series

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Roots of Polynomials

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Maclaurin Series

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Roots of Polynomials

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Maclaurin Series

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Roots of Polynomials

Series

Maclaurin Series

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