SOLUTION: The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−4, The y-intercept is y=−51.2. Find a formula for P(x).

Question 1093636: The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−4, The y-intercept is y=−51.2. Find a formula for P(x).
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
From the roots, the factors are (x-4)^2*(x+4)
when x=0, y=-51.2
(x^2-8x+16)(x+4)=x^3-4x^2-16x+64
but when x=0, y=-51.2
a*(x^3-4x^2-16x+64), when x=0, 64a=-51.2. Therefore, a=-0.8
The equation is -0.8x^3+3.2x^2+12.8x-51.2

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−4, The y-intercept is y=−51.2. Find a formula for P(x).
-----
P(x) = A(x-4)^2(x+4)
-----
Solve for "A" using (0,-51.2)
-----
P(0) = -51.2
-51.2 = A(0-4)^2(0+4)
-51.2 = A*16*4
-51.2 = A*64
A = -51.2/64
---------------------
Ans: P(x) = (-51.2/64)(x-4)^2(x+4)
----------------
Cheers,
Stan H.
-----------
RELATED QUESTIONS
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and. Root of... (answered by josgarithmetic,greenestamps)
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=4 and a root of... (answered by josgarithmetic)
The polynomial of degree 3, P(x) has a root multiplicity 2 at x=1 and a root of... (answered by Boreal)
The polynomial of degree 3, P(x) has a root multiplicity 2 at x=2 and a root of... (answered by ikleyn)
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 1 and a root of... (answered by MathLover1)
The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=5 and a root of... (answered by josgarithmetic)
The polynomial of degree 3 3, P ( x ) P(x), has a root of multiplicity 2 2 at (answered by Alan3354)
The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of... (answered by MathLover1)
The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of... (answered by josgarithmetic)

SOLUTION: The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=&#8722;4, The y-intercept is y=&#8722;51.2. Find a formula for P(x).

SOLUTION: The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−4, The y-intercept is y=−51.2. Find a formula for P(x).