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Quadratics (Identities) Click here to start

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© P. Kavanagh, 2006 Type One Multiply out both sides of the equation. Equate matching coefficients. You may need to solve a set of simultaneous equations. Type Two Solve one equation. The coefficients of the next equation will be equal to one just solved. Put the solutions of the last equation equal to the new unknown expression. Identity Equations

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© P. Kavanagh, 2006 1995 Q1 (a)

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© P. Kavanagh, 2006 2001 Q1 (a)

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© P. Kavanagh, 2006 1997 Q2 (b)

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© P. Kavanagh, 2006 2000 Q2 (b)

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Quadratics (Alpha & Beta, Nature of Roots)

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Quadratic Equation Facts

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© P. Kavanagh, 2006 Roots of a Quadratic

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© P. Kavanagh, 2006 Related Roots

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© P. Kavanagh, 2006 1994 Q2 (b)

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© P. Kavanagh, 2006 1994 Q2 (b) ctd.

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© P. Kavanagh, 2006 1995 Q2 (b) (i)

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© P. Kavanagh, 2006 1996 Q2 (c)

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© P. Kavanagh, 2006 1998 Q1 (c) (part of)

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© P. Kavanagh, 2006 1998 Q2 (b)

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© P. Kavanagh, 2006 2001 Q2 (c)

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© P. Kavanagh, 2006 2002 Q1 (c) (i) Rational: the answer can be expressed as a fraction. Perfect Square: a perfect square has a whole number answer for its root, e.g. 9, 25, 625 are perfect squares whereas 7, 13, 110 are not.

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© P. Kavanagh, 2006 2002 Q1 (c) (ii) Note: Parts (i) and (ii) could both have been answered using this as it can be shown that in fact both of the roots are rational.

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© P. Kavanagh, 2006 2002 Q2 (c) (i)

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© P. Kavanagh, 2006 2002 Q2 (c) (ii)

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© P. Kavanagh, 2006 2003 Q1 (b) (ii)

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© P. Kavanagh, 2006 2003 Q1 (c)

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© P. Kavanagh, 2006 2003 Q2 (c) (ii)

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© P. Kavanagh, 2006 2004 Q2 (b) (ii)

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© P. Kavanagh, 2006 2004 Q2 (c) (i)

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© P. Kavanagh, 2006 2006 Q2 (b)

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3.7 Completing the Square Objective:

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