anonymous
  • anonymous
use rational root theorum and the factor theorem to help solve the following equation x^3+x^2-25x-25
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Mertsj
  • Mertsj
Use synthetic to test the possible rational roots. You will find that -1 works and so x+1 is a factor and x^2+25 is the other factor.
ash2326
  • ash2326
Using the rational root theorem we can guess the roots of an equation The rational roots maybe the factors of constant term over the coefficient of the highest power of x so here the roots maybe \[\frac{\pm 5 , 5,1}{1}\] Let's check if +5 is a root \[x^3+x^2-25x-25\] x=5 \[5^3+5^2-25 \times 5-25=125+25-125-25=0\] so 5 is a root or x-5 is a factor We have now \[x^3+x^2-25x-25\] \[x^2(x-5)+6x(x-5)+5(x-5)\]so we have \[(x^2+6x+5)(x-5)\] In this quadratic x^2+6x+5 the roots maybe given as \[\frac{\pm 5,1}{1}\] Let's check if -5 is a root \[x^2+6x+5=25-30+5=0\] so -5 is a root or x+5 is a factor Let's check -1 is a root, x=-1 \[1-6+5=0\] so (x+1) is also a root the roots are -1, 5 and -5

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