Question

Find the factors from the roots, then multiply the factors together.
y=x3−3.5x2+3.5x−1

Answer 1

hello :

y=x3−3.5x²+3.5x−1

y = (x3 - 1 ) - 3.5 ( x² - 1)

y= (x -1 ) ( x² + x + 1 ) + 3.5 ( x - 1 ) (x + 1)

y = ( x - 1 ) ( x² + x + 1 + 3.5x -3.5)

y = (x - 1 ) ( x² + 4.5x - 2.5)

the dicriminent of x² + 4.5x - 2.5 is : Δ = (4.5)²- 4(1)(- 2.5) = 30.25 = (5.5)²

x1 = ( - 4.5 - 5.5)/2 x2 = ( - 4.5 + 5.5)/2

x1 = - 5 x2 = 1/2 = 0.5

y = (x - 1 )( x +5) (x - 0.5)