Answers:
15) x = 8, [tex]\frac{1}{3}, - \frac{2}{5}[/tex]
16) x = 9, [tex]\frac{5+\sqrt{17}} {2}[/tex], [tex]\frac{5 -\sqrt{17}} {2}[/tex]
17) x = 6, [tex]-\frac{3+i\sqrt{11}} {10}[/tex], [tex]-\frac{3-i\sqrt{11}} {10}[/tex]
Step-by-step explanation:
15x³ - 119x² - 10x + 16 = 0
[tex]\frac{p}{q}: \frac{16}{15}:+/- \frac{1*2*4*8*16}{1*3*5*15}[/tex]
So, the possible rational roots are: +/- [tex]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}[/tex]
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 = [tex]\frac{1}{3}[/tex], x = [tex]-\frac{2}{5}[/tex]
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For #16 & 17, follow the same process as above.
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
