Answer:
x = 0, [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Factorise f(x) and equate to zero for x- intercepts
f(x) = - 5x(9x² - 12x + 4) = 0 ( common factor of - 5x )
To factor the quadratic consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term, that is
product = 9 × 4 = 36 , sum = - 12
The factors are - 6 and - 6
Use these factors to split the middle term
9x² - 6x - 6x + 4 = 0 ( factor the first/second and third/fourth terms )
3x(3x - 2) - 2(3x - 2) ( factor out (3x - 2) )
(3x - 2)(3x - 2), hence
f(x) = - 5x(3x - 2)(3x - 2) = 0
equate each factor to zero and solve for x
- 5x = 0 ⇒ x = 0
(3x - 2)² = 0 ⇒ x = [tex]\frac{2}{3}[/tex] of multiplicity 2, indicating turning point
x - intercepts are x = 0, [tex]\frac{2}{3}[/tex]
