Question

PLEASE HELP!!! h is a polynomial of degree 3. h has a root of multiplicity 2 at c=1, h(−1)=0, and h(0)=−0.19. Find an algebraic equation for h.

Round all answers to 3 decimal place as/if needed.

Answer 1

• h(c) = -0.19(c - 1)²(c + 1)

Explanation:

We need to find an equation of h(c) with the following info given:

• h is of degree 3
• c = 1 is the zero with multiplicity of 2
• h(-1) = 0
• h(0) = - 0.19

According the info above we have factors:

• h(c) = (c - 1)²(kc + t), where k and t unknown for now

Let's work out the value of k and t:

• h(-1) = (- 1 - 1)²(-k + t) = 0 ⇒ - k + t = 0 ⇒ k = t
• h(0) = (0 - 1)²(k*0 + t) = - 0.19 ⇒ t = - 0.19 ⇒ k = -0.19

We now have the factors:

• h(c) = (c - 1)²( - 0.19c - 0.19) ⇒
• h(c) = -0.19(c - 1)² (c + 1)