AQA · Mathematics · 8300
GCSE Maths: Quadratics: formula
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Quadratics: formula (Corbettmaths Video 267), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the quadratic formula?
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x = (−b ± √(b² − 4ac)) / 2a
In the quadratic formula, what does the discriminant refer to?
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The expression b² − 4ac under the square root sign.
When solving a quadratic equation using the quadratic formula, why do we get two solutions?
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Because of the ± symbol, which gives one solution by adding √(b² − 4ac) and another by subtracting it.
Before applying the quadratic formula to an equation like 3x² + 10x + 5 = 7, what must you do first?
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Rearrange it to standard form (ax² + bx + c = 0) by moving all terms to one side.
When rearranging 11x² = 7 − 2x to standard quadratic form, what equation do you get?
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11x² + 2x − 7 = 0
If a rectangular field is w meters wide and 15 meters longer than it is wide, what expression represents its area?
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w(w + 15) or w² + 15w
When solving a word problem that leads to a quadratic equation with two solutions, one positive and one negative, which solution should you typically use for a length measurement?
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The positive solution, since length cannot be negative.
If you arrive at x = (5 ± √53) / 2 when solving x² + bx + c = 0, what is the value of b?
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b = −5
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