1,307 prompts matching "Derive the quadratic formula"
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Learn: The degree of a polynomial and its leading coefficient
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Quiz: The factor theorem, and testing whether x minus a is a factor
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Explain Back: Finding an unknown coefficient given that a stated factor divides the polynomial
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Spot My Mistake: The factor theorem for a divisor of the form ax minus b
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Final Revision: The zeros of a polynomial and where its graph cuts the x-axis
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Learn: The sum of the roots of a cubic read from its coefficients
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Worked Example: The sum of the products of the roots of a cubic taken two at a time
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Quiz: The product of the roots of a cubic
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Practice: Finding the third root of a cubic when two are known
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Spot My Mistake: The relations between roots and coefficients for a quartic
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Final Revision: Checking that the roots found satisfy the original equation
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Learn: Solving a linear inequality, and reversing the sign on dividing by a negative
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Practice: Solving an inequality with the unknown in the denominator
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Spot My Mistake: Showing the solution of an inequality on a number line
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Common Mistakes: The range of values of x for which an expression stays positive
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Final Revision: The region of the plane satisfying a set of linear inequalities
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Learn: The meaning of n factorial, and how to evaluate it
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Worked Example: The number of arrangements of n different objects in a row
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Quiz: The number of arrangements of r objects chosen from n
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Practice: Arrangements when some of the objects are identical
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