Test: Quadratic equations

Dynamic incomplete and complete quadratic equations, discriminants, root counts and word modelling.

Question qty: 10
Duration in minutes: 21
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Sample questions

How many real solutions does x² + (b)x + (c) = 0 have?
Solve x² = c.
Calculate the discriminant of ax² + (b)x + (c) = 0.
Solve ax² + (b)x = 0.
Solve x² + (b)x + (c) = 0.
Is x a root of x² + (b)x + (c) = 0?
A rectangle has area s, and its length is d units greater than its width. Find width and length.
Which quadratic equation has roots x1 and x2?

Quadratic equations

A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0. The discriminant D = b² − 4ac determines the number of real roots: two when D > 0, one when D = 0 and none when D < 0.

Methods of solution

Use x = (−b ± √D)/(2a), factorisation or completing the square. Incomplete equations can often be solved more directly. Substitute roots into the original equation and handle brackets carefully, especially when b is negative.

Test: Quadratic equations

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Question Nr. 10 out of 10

Sample questions

Quadratic equations

Methods of solution

Test: Quadratic equations

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

Question Nr. 6 out of 10

Question Nr. 7 out of 10

Question Nr. 8 out of 10

Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Quadratic equations

Methods of solution

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