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Flashcards · Maths · Further Algebra

Solving Quadratic Equations

16 cards

  1. What fact makes solving by factorising work?

    If two things multiply to give zero, one of them must be zero.

  2. What is the first step when solving a quadratic by factorising?

    Rearrange so that one side is zero.

  3. Solve \((x - 2)(x - 3) = 0\).

    \(x = 2\) or \(x = 3\).

  4. Solve \(x^2 - 49 = 0\).

    \(x = 7\) or \(x = -7\).

  5. Solve \(x^2 - 6x = 0\).

    \(x = 0\) or \(x = 6\).

  6. Why should you not divide both sides of \(x^2 = 6x\) by \(x\)?

    You lose the solution \(x = 0\).

  7. Factorise \(x^2 - 5x + 6\).

    \((x - 2)(x - 3)\).

  8. How do you factorise \(2x^2 + 7x + 3\)?

    Multiply \(a\) and \(c\) to get 6, split the middle term into \(6x + x\), and factorise in pairs to get \((2x + 1)(x + 3)\).

  9. How are the solutions of a quadratic linked to its graph?

    They are the \(x\)-values where the graph crosses the \(x\)-axis.

  10. What is the quadratic formula (Higher tier)?

    \(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

  11. What is the discriminant (Higher tier)?

    \(b^2 - 4ac\), the number under the square root.

  12. What does a negative discriminant mean (Higher tier)?

    There are no real solutions.

  13. Complete the square for \(x^2 + 6x\) (Higher tier).

    \((x + 3)^2 - 9\).

  14. Why might you reject one solution of a quadratic?

    It may not make sense in the problem, such as a negative length.

  15. How do you check the solutions?

    Substitute each one back into the original equation.

  16. What does a repeated root look like on a graph?

    The curve just touches the \(x\)-axis.