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)

Algebra ->  Polynomials-and-rational-expressions -> 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)      Log On


   

Question 1118793: f(x)=+x%5E3%2B3x%5E2%2B2x%2B5+
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(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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f(x)=+x%5E3%2B3x%5E2%2B2x%2B5+
(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) = %28x%2B7%29%5E3+%2B+3%2A%28x%2B7%29%5E2+%2B+2%2A%28x%2B7%29+%2B+5.


              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) = 4%5E3%2A%28%28x%2F4%29%5E3+%2B+3%2A%28x%2F4%29%5E2+%2B+2%2A%28x%2F4%29+%2B+5%29.


               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.