Answer to Question #171671 in Algebra for Moel Tariburu

Question

Determine the x-intercepts of a cubic function y= x² - 2x²- 5x + 6

Answer 1

y = x³ - 2x² - 5x + 6

$y = 1² - 2(1)² - 5(1) + 6\\ y = 1 -2 -5 +6\\ y = 0\\$

$\therefore$ x= 1 is an intercept on the x axis

$\dfrac{x³ - 2x² - 5x + 6}{x-1 } = x² - x - 6$

$x² - x - 6 = (x -3)(x+2)$

$\therefore$ the x - intercepts of the cubic function are -2, 1 and 3