A Level H2 Maths 2012 Paper 2 Q3 Solution; H2 Maths Tuition

A Level H2 Maths 2012 Paper 2 Q3 Solution

(i)

cubic graph maths tuition

(The graph above is drawn using the Geogebra software 🙂 )

(ii)

x^3+x^2-2x-4=4

x^3+x^2-2x-8=0

By GC, x=2

By long division, x^3+x^2-2x-8=(x-2)(x^2+3x+4)

The discriminant of x^2+3x+4 is

D=b^2-4ac=3^2-4(1)(4)=-7<0

Hence, there are no other real solutions (proven).

(iii) x+3=2

x=-1

(iv)

cubic absolute graph maths tuition

(v)

|x^3+x^2-2x-4|=4

x^3+x^2-2x-4=4 or x^3+x^2-2x-4=-4

x^3+x^2-2x-8=0 or x^3+x^2-2x=0

x^3+x^2-2x-8=0 \implies x=2 (from part ii)

x^3+x^2-2x=x(x^2+x-2)=x(x-1)(x+2)=0

x=0,1,-2

In summary, the roots are -2,0,1,2