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SingaporeAdditional MathematicsQuick questions

Quadratic Functions and Equations

Quick questions on The discriminant and nature of roots explained: O-Level A-Maths

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are finding unknown constants?
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A typical problem gives a quadratic with an unknown kk and a condition on the roots. Translate the condition into a statement about Δ\Delta, then solve the resulting equation or inequality for kk.
What is wrong inequality for the condition?
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Distinct roots is Δ>0\Delta > 0; equal roots is Δ=0\Delta = 0; real roots (at least one) is Δ≥0\Delta \geq 0.
What is q1?
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State the nature of the roots of x2+4x+4=0x^2 + 4x + 4 = 0. [2 marks]
What is q2?
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Find kk if kx2+4x+1=0kx^2 + 4x + 1 = 0 has equal roots. [3 marks]
What is q3?
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For what values of mm does x2+mx+1=0x^2 + mx + 1 = 0 have no real roots? [3 marks]

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