SOLUTION: f(x)={{{ x^3+3x^2+2x+5 }}} find the monic polynomial g(x) whose roots are 7 units to the left of f(x) find the monic polynomial h(x) whose roots are 4 times the roots of f(x)

Question 1118793: f(x)=
find the monic polynomial g(x) whose roots are 7 units to the left of f(x)
find the monic polynomial h(x) whose roots are 4 times the roots of f(x)
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
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f(x)=
(a) find the monic polynomial g(x) whose roots are 7 units to the left of f(x)
(b) find the monic polynomial h(x) whose roots are 4 times the roots of f(x)
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(a) find the monic polynomial g(x) whose roots are 7 units to the left of f(x)

     Answer.  g(x) = .


              If "x" is the root of f(x), then (x-7), which is 7 units to the left from "x", is the root to g(x),

              i.e. satisfies the given requirement.

(b) find the monic polynomial h(x) whose roots are 4 times the roots of f(x)

     Answer.   h(x) = .


               If "x" is the root of f(x), then 4x, which is 4 times "x", is the root to h(x),  and h(x) is a monic polynomial,

               i.e. satisfies all the given requirements.

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