Target Mathematics

1.2: Equations and inequalities

4PM1/2/June/2024 — Question 1 · 6 marks

f(x)=6x313x2+ax10wherea is a constantf(x) = 6x^3 - 13x^2 + ax - 10 \quad \mathrm{where} a \text{ is a constant}
Given that (3x2)(3x - 2) is a factor of f(x)f(x)
(a) show that a=21a = 21
(2)
(b) Hence show algebraically that the curve y=f(x)y = f(x) has only one intersection with the xx-axis.
(4)