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Polynomials

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asked Oct 28, 2014 in CALCULUS by zoe Apprentice

1 Answer

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The polynomial f(x) = 2x3 - 5x2 + ax + b

1 as a root.

So the remainder is zero.

f(1) = 2(1)- 5(1)2 + a(1) + b

0 = 2 - 5 + a + b

- 2 + 5 = a + b

a + b = 3 ---> (1)

 

From remainder theorem,

When you divide a polynomial f(x) by x - a the remainder r will be f(a).

The remainder 16 when divided by x -  4.

f(4) = 2(4)- 5(4)2 + a(4) + b

16 = 128 - 80 + 4a + b

16 - 128 + 80 = 4a + b

4a + b = - 32 ---> (2)

 

Now solve the equations (1) and (2) in Gauss reduction method.

Write the equations into matrices form AX = B

A is coefficient matrix, X is variable matrix and B is constant matrix.

image

The augmented matrix is image

image are represents first row, second row.

 

image

image

image

image

image

image

image

Substitute the a, b values in polynomial function f(x) = 2x3 - 5x2 + ax + b

f(x) = 2x3 - 5x2 - (35/3)x + (44/3).

answered Oct 28, 2014 by david Expert
edited Oct 28, 2014 by david

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