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Welcome to GCSE Edexcel Maths revision.

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Topic M 15: Quadratic equations.

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This video covers Higher tier.

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It includes the shared content and the labelled Higher extensions.

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A quadratic equation contains a squared unknown as its highest power.

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Write it as a x squared plus b x plus c equals 0, where a is not equal to 0, before choosing a solution method.

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If two factors multiply to zero, at least one factor must be zero.

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This zero-product rule applies to a product, not a sum.

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Worked example: x squared plus 5 x plus 6 equals 0 becomes open bracket x plus 2 close bracket multiplied by open bracket x plus 3 close bracket equals 0.

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Therefore x equals minus 2 or x equals minus 3.

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Check each in the original equation.

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Worked example: x squared equals 5 x gives x squared minus 5 x equals x multiplied by open bracket x minus 5 close bracket equals 0, so x equals 0 or x equals 5.

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Dividing straight away by x would lose the zero solution.

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For x squared equals 49, x equals plus or minus 7.

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Taking a square root without considering both signs can lose a solution.

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Use a graph of y equals a x squared plus b x plus c to find approximate roots at the x-axis.

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A parabola may have two, one repeated, or no real roots.

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Roots of x squared plus five x plus six

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Worked example: A rectangle has width x cm and length x plus 3 centimetres,

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and area 28 square centimetres . x multiplied by open bracket x plus 3 close bracket equals 28 gives open bracket x plus 7 close bracket multiplied by open bracket x minus 4 close bracket equals 0.

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Only x equals 4 centimetres is a valid width; a negative length is rejected with a reason.

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Do not discard a negative algebraic solution unless the context rules it out.

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Coordinates, temperatures and some other quantities can be negative.

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When using an approximate root, retain enough precision for subsequent work and round the final contextual answer appropriately.

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For x squared plus b x,

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add and subtract open bracket the fraction with numerator open bracket b close bracket and denominator open bracket 2 close bracket ,

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end fraction close bracket squared to create a square. x squared plus 6 x plus 5 equals open bracket x plus 3 close bracket squared minus 4.

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Worked example: x squared plus 6 x plus 5 equals 0 gives open bracket x plus 3 close bracket squared equals 4, so x plus 3 equals plus or minus 2 and x equals minus 1 or minus 5.

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For a x squared plus b x plus c equals 0,

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x equals the fraction with numerator open bracket minus b plus or minus square root of open bracket b squared minus 4 a c close bracket close bracket and denominator open bracket 2 a close bracket ,

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end fraction .

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The denominator divides the whole numerator, including the square-root term.

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Worked example: 2 x squared minus 3 x minus 1 equals 0 has a equals 2,

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b equals minus 3,

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c equals minus 1. x equals the fraction with numerator open bracket 3 plus or minus square root of 17 close bracket and denominator open bracket 4 close bracket ,

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end fraction is approximately equal to 1.781 or minus 0.281.

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Use brackets around negative substitutions.

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The discriminant b squared minus 4 a c is positive for two distinct real roots, zero for a repeated root and negative for no real roots.

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GCSE real-number work cannot take the square root of a negative discriminant.

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Choose an efficient method: factorise where possible, use completing the square for exact structure, or use the formula for a general quadratic.

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A calculator result still needs clear working when asked.

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That completes Quadratic equations.

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Revisit the notes and test yourself on the revision website.