1,042 prompts matching "Combining several index laws in one simplification"
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Spot My Mistake: Completing the square when the roots are not real
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Final Revision: Why completing the square always works
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Learn: Deriving the quadratic formula by completing the square
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Worked Example: Substituting a, b and c into the quadratic formula correctly
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Quiz: A negative value of b in the quadratic formula
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Explain Back: Leaving the roots of a quadratic in surd form
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Spot My Mistake: What the formula gives when the discriminant is nought
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Final Revision: A word problem solved with the quadratic formula
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Learn: The sum of the roots as minus b over a
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Quiz: Finding the sum and the product without solving the equation
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Explain Back: Finding a missing coefficient from a stated sum of roots
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Spot My Mistake: Finding a missing coefficient from a stated product of roots
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Common Mistakes: Roots that are reciprocals of one another
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Learn: What makes an expression in the roots symmetric
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Worked Example: The identity linking alpha squared plus beta squared to the sum and product
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Quiz: The value of one over alpha squared plus one over beta squared
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Explain Back: The value of alpha minus beta, all squared
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Final Revision: Using a symmetric function to find an unknown coefficient
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Worked Example: Substituting into the quadratic and tidying up
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Quiz: Solving the quadratic that results from the substitution
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