Question

Solve each polynomial equation.

Answer 1

Answers:

15) x = 8, $\frac{1}{3}, - \frac{2}{5}$

16) x = 9, $\frac{5+\sqrt{17}} {2}$, $\frac{5 -\sqrt{17}} {2}$

17) x = 6, $-\frac{3+i\sqrt{11}} {10}$, $-\frac{3-i\sqrt{11}} {10}$

Step-by-step explanation:

15x³ - 119x² - 10x + 16 = 0

$\frac{p}{q}: \frac{16}{15}:+/- \frac{1*2*4*8*16}{1*3*5*15}$

So, the possible rational roots are: +/-   $1, 2, 4, 8, 16,\frac{1}{3},\frac{2}{3},\frac{4}{3},\frac{8}{3},\frac{16}{3},\frac{1}{5},\frac{2}{5},\frac{4}{5},\frac{8}{5},\frac{16}{5},\frac{1}{15},\frac{2}{15},\frac{4}{15},\frac{8}{15},\frac{16}{15}$

Use synthetic division with each one until you find a remainder of zero.  I am not going to go through each one because it is too time consuming, however, the first one that works is x = 8

(x - 8)(15x² + x - 2)    

Next, factor 15x² + x - 2 using any method

(x - 8)(3x - 1)(5x + 2)

Now, solve for x.

x = 8, x = $\frac{1}{3}$, x = $-\frac{2}{5}$

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For #16 & 17, follow the same process as above.

Answer 2

Answer:

15.   8, - 0.4 and  0.333 to nearest thousandth.

Step-by-step explanation:

15.   as the last  value is 16 we might try  x = 4 and x = 8 as roots

f(4) = -968  - Not a root . f(8) = 0  so x = 8 is one root and x - 8 is a factor

If we divide  the function by x - 8 we get   15x^2  + x - 2

which factors to  (5x  + 2)(3x -  1)

(5x + 2)(3x - 1) = 0  giving x = -0.4 and x = 1/3.

So the roots are 8, -0.4 and  1/3