1,032 prompts matching "Teach me Cramer's rule from first principles"
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Solve 3x^2 - 5x - 2 = 0 by factorisation
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Solve x^2 - 6x + 9 = 0 by factorisation
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Solve 2x^2 - 11x + 5 = 0 by factorisation
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Solve x^2 + x - 12 = 0 by factorisation
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Discriminant and the nature of roots
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Sum and product of roots of a cubic equation
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Worked example: differentiate y = 3x^4 - 2x^3 + x - 7
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Worked example: find the gradient of y = x^3 - 4x at the point where x = 2
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Worked example: find the stationary points of y = x^3 - 3x^2 - 9x + 5 and classify each one
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Worked example: find the equation of the tangent to y = x^2 - 5x + 6 at the point where x = 1
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Learn: Factorising a quadratic whose coefficient of x squared is one
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Practice: Working through a quadratic by completing the square, step by step
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Learn: Deriving the quadratic formula by completing the square
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Practice: Giving the roots correct to two decimal places
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Learn: The sum of the roots as minus b over a
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Practice: The value of alpha to the fourth plus beta to the fourth
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Learn: Making one unknown the subject of the linear equation
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Practice: Finding the matching value of the second unknown
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Practice: The condition for the line to be a tangent
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Learn: What makes an expression a polynomial
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