Quadratic formula
AQA GCSE Maths revision on Quadratic formula. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
Before applying the quadratic formula to the equation 3x - 5 = 2x^2, what is the mandatory first step?
- A) Divide the entire equation by 3
- B) Rearrange the equation into the form ax^2 + bx + c = 0
- C) Calculate the square root of the constant term
- D) Factorise the left hand side
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Answer: Rearrange the equation into the form ax^2 + bx + c = 0
The quadratic formula is derived specifically for the standard form ax^2 + bx + c = 0. If the equation is not in this form, the values of a, b, and c will be incorrect, leading to an invalid result. Always ensure all terms are moved to one side before identifying the coefficients.
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Question 2
When using the quadratic formula, what does the value of the discriminant (b^2 - 4ac) tell you about the roots?
- A) The gradient of the curve
- B) The number and nature of the real solutions
- C) The y-intercept of the parabola
- D) The distance between the two roots
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Answer: The number and nature of the real solutions
If b^2 - 4ac is positive, there are two distinct real roots. If it is zero, there is exactly one repeated real root, and if it is negative, there are no real roots because you cannot square root a negative number in the real number system.
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Question 3
A student attempts to solve 2x^2 + 8x + 4 = 0 and sets a=2, b=8, c=-4. What is their error?
- A) They should have divided by 2 first
- B) They misidentified the sign of the constant term c
- C) They should have squared b before multiplying by 4
- D) They misidentified the coefficient of x
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Answer: They misidentified the sign of the constant term c
In the standard form ax^2 + bx + c = 0, the sign of the constant term is part of the value of c. Since the equation was 2x^2 + 8x + 4 = 0, the value of c is positive 4, not negative 4. Failing to account for signs is the most common cause of errors in the quadratic formula.
Want to test yourself on the remaining cards for this topic?
13 more questions on Quadratic formula — plus mistakes tracking and spaced repetition across the whole Maths spec.