polynomial (1 Viewer)

[enigma_1]

A polynomial of degree 3 has a double zero at 2. When x = 1 it takes the value 6 and
when x = 3 it takes the value 8. Find the polynomial.

 

[Trebla]

From the information we can deduce that
P(x) = a(x - 2)²(x - k)
P(1) = 6
P(3) = 8

Use the last two conditions to solve for a and k

 

[IceKool15]

Hi there!

Solved it:

P(x) = (x-2)²(x+5)

We have a cubic poly. Since it is deg 3.

Using Trebla's explanation, we get the following:

When x = 1,
(a - b)(-1)² = 6 => (a - b) = 6 --------------------------(Equation 1)

When x = 3,
(3a - b) = 8 ----------------------------(Equation 2)

Now, you have 2 equations, simply solve simultaneously using Eqn (1) and (2).

a = 1, b = -5,

 

[hit patel]

trebla would the dy/dx due to double root and then simultaneous work?