AQA · Mathematics · 8300

GCSE Maths: Quadratics: solving (foundation)

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Quadratics: solving (foundation) (Corbettmaths), 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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  1. How do you solve a quadratic equation in factored form, such as (x − 2)(x + 9) = 0?

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    Set each factor equal to zero and solve. For (x − 2)(x + 9) = 0, the solutions are x = 2 and x = −9.

  2. What are the roots of the equation (x − 6)(x + 1) = 0?

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    x = 6 and x = −1

  3. What is the first step to solve x² + 5x + 6 = 0?

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    Factor the quadratic into (x + 2)(x + 3) = 0, then set each factor equal to zero.

  4. What are the solutions to x² − 49 = 0?

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    x = 7 and x = −7. This is a difference of two squares: (x − 7)(x + 7) = 0.

  5. If x² + bx + c = 0 has solutions x = −8 and x = −2, what is the value of b?

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    b = 10. The factored form is (x + 8)(x + 2) = 0, which expands to x² + 10x + 16 = 0.

  6. If x² + bx + c = 0 has only one solution x = −3, what are the values of b and c?

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    b = 6 and c = 9. A repeated root means (x + 3)² = 0, which expands to x² + 6x + 9 = 0.

  7. How do you solve y² − 6y = 27?

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    Rearrange to standard form: y² − 6y − 27 = 0. Factor to (y − 9)(y + 3) = 0, giving y = 9 or y = −3.

  8. What must you do before solving x² = 8x − 15?

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    Rearrange to standard form by moving all terms to one side: x² − 8x + 15 = 0.

  9. Victor is y years old and his brother Fred is 4 years older. If the product of their ages is 780, what equation represents this?

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    y(y + 4) = 780 or y² + 4y = 780

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