Question

The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 2 and a root of multiplicity 1 at x = − 3 . The y -intercept is y = − 8.4 . Find a formula for P ( x ) . P ( x ) =

Answer 1

P ( x ) = -0.7 (x - 2)²(x + 3)

Explanation:

We are given :

P ( x ) , has a root of multiplicity 2 at x = 2

and a root of multiplicity 1 at x = − 3

Then

P ( x ) = a (x - 2)²(x + 3) ; where ‘a’ is a real number.

P ( x ) = a (x - 2)²(x + 3)

= a (x² - 4x + 4)(x + 3)

= a [x³ - 4x² + 4x + 3x² - 12x + 12]

P (0) = -8.4

⇔ a [(0)³ - 4(0)² + 4(0) + 3(0)² - 12(0) + 12] = -8.4

⇔ 12 a = -8.4

⇔ a = (-8,4) ÷ 12

⇔ a = -0,7

Conclusion :

P ( x ) = -0.7 (x - 2)²(x + 3)