Discriminant and exact roots

Practise discriminant and exact roots with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

Consider $2x^2-3x-3=0$. (a) Find the discriminant and state the number of real roots. [1 marks] (b) Find both roots exactly. [2 marks]

Worked explanation

• Part (a)

  $\Delta=b^2-4ac=9-4(2)(-3)=33>0$, so there are two distinct real roots.

• Part (b)

  The quadratic formula gives $x=\frac{-b\pm\sqrt\Delta}{2a}=\frac{3\pm\sqrt{33}}4$.

(a) $33$; two distinct real roots.; (b) $x=(3\pm\sqrt{33})/4$.

Original VectorPaths practice; not an official VCAA question or marking rubric.