Test
Quadratic equations
Dynamic incomplete and complete quadratic equations, discriminants, root counts and word modelling.
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Question 1out of 10
An equation root is a value of x that makes the equation true when substituted for x.
For this question, you do not need to solve the whole equation. Substitute the given number for every x and calculate the left-hand side:
x2 + bx + c.
- Square the given number.
- Multiply the given number by the coefficient b.
- Add c and combine all the resulting numbers.
If the result is 0, the given number is a root of the equation. If the result is not 0, it is not a root.
When the roots of a quadratic equation must be found, first calculate the discriminant D = b2 − 4ac, then use x = (−b ± √D) / 2a.
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Question 9out of 10
An equation root is a value of x that makes the equation true when substituted for x.
For this question, you do not need to solve the whole equation. Substitute the given number for every x and calculate the left-hand side:
x2 + bx + c.
- Square the given number.
- Multiply the given number by the coefficient b.
- Add c and combine all the resulting numbers.
If the result is 0, the given number is a root of the equation. If the result is not 0, it is not a root.
When the roots of a quadratic equation must be found, first calculate the discriminant D = b2 − 4ac, then use x = (−b ± √D) / 2a.
Question 10out of 10
The discriminant is an expression formed from the coefficients of a quadratic equation ax² + bx + c = 0. It helps determine the number of real solutions.
Formula: D = b² − 4ac.
- Identify the coefficients a, b and c, paying attention to their signs.
- Calculate b².
- Calculate 4ac and subtract it from b².
If D > 0, the equation has two real solutions; if D = 0, it has one; if D < 0, it has no real solutions.
Time left: 00:00:00
Sample questions
- Solve x² = ___.
- Solve ___x² + (___)x = 0.
- Calculate the discriminant of ___x² + (___)x + (___) = 0.
- Solve x² + (___)x + (___) = 0.
- How many real solutions does x² + (___)x + (___) = 0 have?
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.
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