In the polynomial f(x) =2*x^4 - 49*x^2 +54, what is the product of the roots, and what is the sum of the roots (Note that x^n denotes the x raised to the power n, or x multiplied by itself n times)?

• sum of roots= -(coeff of x^3/coeff of x^4)= -b/a = -0/2=0
  product of roots=(-1)^n*(coeff of constant term/coeff of x^4)= e/a = 54/2 =27
• 11 years agoHelpfull: Yes(155) No(1)
• Adding the roots gives -b/a
  Multiplying the roots gives (where "c" is the constant at the end):
  c/a (for even degree polynomials like quadratics)
  -c/a (for odd degree polynomials like cubics)
  Here polynomial is of even degree
  ie.
  product of roots= 54/2= 27
  and sum of roots 0 as coefficeint of x^3=0
• 11 years agoHelpfull: Yes(40) No(2)
• answer: sum-0; product:27
  sum of roots= -b/a = -coefficient of (n-1)th degree term/coefficient of nth degree term
  =-0/2=0
  product of roots= c/a= constant term/coefficient of nth degree term
  =54/2=27
• 9 years agoHelpfull: Yes(8) No(0)
• sum of the roots=-b/a=>-0/a=>0
  product of the roots=c/a=>54/2=27
• 11 years agoHelpfull: Yes(3) No(1)
• Sum 0 since x^3 gayab , while product = 27 Ans.
• 11 years agoHelpfull: Yes(3) No(2)
• maa chudaaoo
• 9 years agoHelpfull: Yes(3) No(17)
• @manoj.....here b is the coeff of x^3 not of x^2 so for the sum of root it will be 0/2 not 49/2 that you written...:(
• 11 years agoHelpfull: Yes(2) No(1)
• sum of roots=49/2 bcoz---sum =(-b/a)
  product of roots = 54/2
  bcoz---sum =(c/a) {here it is highest degree of eqn is even}
• 11 years agoHelpfull: Yes(1) No(10)
• 27,0 as prod=c/a nd sum=-b/a
  
• 11 years agoHelpfull: Yes(1) No(0)
• sum of root is -ve coeff of x^3/coeff. of x^3
  i.e 0
  and product of root is coeff of const/coeff of x^3
  i.e 54/2=17
  
• 11 years agoHelpfull: Yes(0) No(12)