Solving Quadratic Equations (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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Why does $(x - 3) (x + 7) = 0$ mean that either $x - 3 = 0$ or $x + 7 = 0$ ?
Because if two things multiply together to give zero, at least one of them must itself be zero.
Each bracket is therefore set equal to zero in turn and solved separately.
Complete the two solutions of $(x + 4) (x - 1) = 0$ , taking the brackets in order:
$x =______$ or $x =______$
The completed solutions are:
$x = - 4$ or $x = 1$
Each solution is the number in its bracket with the opposite sign.
Solve $x (x - 4) = 0$ .
$x = 0$ or $x = 4$ .
The lone $x$ counts as a factor in its own right, so setting it equal to zero gives the solution $x = 0$ .
True or False?
$x^{2} - x = 0$ can be solved by dividing both sides by $x$ to give $x - 1 = 0$ .
False.
Dividing both sides by $x$ removes a whole factor from the equation, and one of its two solutions goes with it.
Factorise instead: $x (x - 1) = 0$ keeps both.
Solve $x^{2} + 3 x - 10 = 0$ .
$x = 2$ or $x = - 5$ .
The left-hand side factorises to $(x - 2) (x + 5)$ , and the equation already has zero on the right.

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