IB Maths AA SL 2.7 Quadratic equations and inequalities Question Bank

Practise IB Maths AA SL 2.7 by solving quadratic equations and inequalities with roots, graphs and discriminants.

Exam points

Solve a quadratic equation by factoring, completing the square or using the quadratic formula.
Use a discriminant to determine the number and type of real roots.
Solve a quadratic inequality and express the valid interval using a graph or interval notation.

[Maximum number: 4]

Let $f(x)=3 x^{2}-6 x+p$ . The equation f(x)=0 has two equal roots.

(a)

Write down the value of the discriminant.

[ 1 ]

correct value 0 , or $36-12 p \quad \boldsymbol{A}^{2}$

(b)

Hence, show that p=3.

[ 2 ]

correct equation which clearly leads to $p=3 \quad \boldsymbol{A} \mathbf{1}$
eg $\quad 36-12 p=0,36=12 p$
p=3
AG N0

(c)

Write down the solution of f(x)=0.

[ 1 ]

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