quadratic equation - task

task - an inquiry to solving all quadratic equations 1:

$${ax^2 + bx + c = 0}$$

Solve each of the following equations.

As a general rule, each equation has got two (!) solutions.

Write down all your thoughts in your notes and comment about how the question differs from the previous one. Make sure not to expand the term in exercise no 5 and use no 5 to solve no 6.

You do not have to solve all at once. You will be given plenty of time.

Where you have square roots, make sure that

questions

no 1

$${x^2 = 4}$$

no 2

$${x^2 - 3 = 0}$$

no 3

$${2x^2 - 1 = 0}$$

no 4

$${x^2 = 6}$$

no 5

$${(x + 2)^2 = 6}$$

no 6

$${x^2 - 6x + 9 = \frac{25}{4}}$$

no 7

$${x^2 -6x = 31}$$

no 8

$${x^2 + 4x = - \frac{7}{4}}$$

no 9

$${x^2 - \frac{2}{3}x = - \frac{1}{9}}$$

no 10

$${x^2 - 3x = - \frac{25}{4}}$$

no 11

$${2x^2 + 4x - 7 = 0}$$

no 12

$${\frac{1}{6}x^2 - \frac{1}{4}x - \frac{1}{6} = 0}$$

no 13

$${x^2 + 2px + q = 0}$$

no 14

$${ax^2 + bx + c = 0}$$

Solving question no 14 leads to the quadratic formula.

different question no 13 for the pq-formula derived in Berlin

no 13b (berlin)

$${x^2 + px + q = 0}$$


  1. Towards New Teaching in Mathematics, Issue 5, Peter Gallin, The Quadratic Equation – This is a Topic to Be Taught in an Inquiry-Based Way After All, Bayreuth, Germany, 2011, translation - Maren Distel, Singen [return]

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