Ask Question
3 August, 15:00

The polynomial of degree 3, P (x), has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=-2. The y-intercept is y=-9.6

Find a formula for P (x)

+2
Answers (1)
  1. 3 August, 16:56
    0
    Multiplicity is hoa many times it repeats

    example

    if you have roots, r1 multiplicity 2 and r2 multiliicty 3 the factors are

    f (x) = (x-r1) ^2 (x-r2) ^3

    so

    multiplicty 2 at x=4

    multilicty 1 at x=-2

    (x-4) ^2 (x - (-2)) ^1=

    (x-4) ^2 (x+2))

    expand

    x^3-6x^2+32

    remember

    for roots, r1 and r2

    (x-r1) (x-r2)

    the roots don't change if you multiply whold thing by a unless a=0

    so

    the yint is where x=0

    so the yint now is 32

    32 times what=-9.6?

    divide both sides by 32

    what=-0.3

    the polynomial is

    p (x) = - 0.3 (x-4) ² (x+2)

    expanded is

    p (x) = - 0.3x³+1.8x²-9.6
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “The polynomial of degree 3, P (x), has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=-2. The y-intercept is y=-9.6 Find ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers