In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers. If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)?

a. 3-sqrt(7)

b. 3+sqrt(21)

c. 5

d. sqrt(7) + sqrt(3)

Sol: Option A

• we have have read befre that roots are imaginary and contains both +/- in it so as 1 is 3+sqrt7 so othr will be 3-sqrt7. (ans)
• 9 years agoHelpfull: Yes(17) No(2)
• room pr aaa ja
  
• 9 years agoHelpfull: Yes(7) No(15)
• complex roots always exist in conjugate pair...
  so
  a. 3-sqrt(7) will be the answer
• 9 years agoHelpfull: Yes(6) No(2)
• here,
  taking option a.
  sum of roots=(-a/1)=(3+sqrt7)+(3-sqrt7)=6....therefore a=-6(an integer value)
  and product of roots=(-d/1)=(3+sqrt7)(3-sqrt7)=9-7=2....therefore d=-2(an integer value)
  No other options satisfy the condition of a and d to be integer values.
• 8 years agoHelpfull: Yes(4) No(1)
• Koi to samkha do. Please
  
• 9 years agoHelpfull: Yes(1) No(4)
• in quad eqn p(x)= ax^2+ bx+c (here p is polynomial) the roots are
  alpha= -b+sqrtD/2a and beta= -b-sqrtD/2a
  d=-b+2ac so if a polynomial has one root= x-sqrt7 that means other root will be x+sqrt7
• 6 years agoHelpfull: Yes(1) No(0)
• 3-sqrt(7)
• 9 years agoHelpfull: Yes(0) No(3)
• Plz explain
• 8 years agoHelpfull: Yes(0) No(1)
• as sum of two roots=-b/a
  so here its -b
  and also -b=1 root+2 root
  -b=3+sqrt(7)+2 root
  so 2 root=-b-3-sqrt(7)
  which means in answere there must be -sqrt(7)
  ie answere is 3-sqrt(7)
• 8 years agoHelpfull: Yes(0) No(0)