Unit 2: Functions
Topic 2.7: Solving Quadratics Questions
Practice 20 exam-style questions for IB Math AA SL Topic 2.7. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2025
At any point common to the line and the curve , the -coordinate obeys a quadratic. Derive it and confirm it is .
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2026
Find the discriminant of and state the number of real roots.
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2026
Find the discriminant of 3x2 − 5x + 2 and state the number of real roots.
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2026
Show that x2 + 2x + 5 = 0 has no real roots.
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A parabola opens upward and has roots at and , where . Where is negative?
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2026
Write down the number of real roots.
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2024
Show that has exactly one -intercept.
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2025
Consider f(x) = ½x2 + kx + 8, where k ∈ ℤ+.
Given that the equation f(x) = 0 has no real roots, show that the greatest possible value of k is 3.
Given that the equation f(x) = 0 has no real roots, show that the greatest possible value of k is 3.
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2024
Show that when and , the equation has two distinct real roots.
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2025
At any point common to the line and the curve , the -coordinate obeys a quadratic. Derive it and confirm it is .
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