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IB Maths AA SL 2.7 Quadratic Equations and Inequalities

IB Maths AA SL 2.7 Quadratic Equations and Inequalities
IB Mathematics: analysis and approaches guide, first assessment 2021

Practise solving quadratic equations and inequalities and using the discriminant, root signs and tangent conditions to determine solution intervals or parameter restrictions.

How this is tested

  • solve a quadratic by factorisation, completing the square or formula and check all stated restrictions
  • use a sign diagram or parabola to select the intervals satisfying a quadratic inequality
  • set the discriminant to zero for tangency or use its sign to restrict the number and type of roots

Question 7(c)(i)

Consider a triangle PQR where PR=3, QR=2 and PR^Q=60∘\mathrm{P} \hat{\mathrm{R}} \mathrm{Q}=60^{\circ}.

Figure for Question 7(c)(i) — IB Maths AA SL

Given that AB=7,

find the value of x;