High School

Does [tex]x = -5[/tex] solve the following polynomial equation?

[tex]4x^7 - 101x^5 = 9x^4 - 100x^2[/tex]

Answer :

Yes, x=-5 solves the polynomial equation 4x⁷ - 101x⁵ = 9x⁴ - 100x². Both sides of the equation are equal when x=-5 is substituted.

To determine if x=-5 solves the polynomial equation 4x⁷ - 101x⁵ = 9x⁴ - 100x², we need to substitute x=-5 into the equation and simplify both sides.

  1. First, substitute x=-5 into the left-hand side (LHS) of the equation:
  2. LHS = 4(-5)⁷ - 101(-5)⁵
  3. Simplify the powers and coefficients:
  4. LHS = 4(-78125) - 101(-3125)
  5. LHS = -312500 + 315625
  6. LHS = 3125
  7. Next, substitute x=-5 into the right-hand side (RHS) of the equation:
  8. RHS = 9(-5)⁴ - 100(-5)²
  9. Simplify the powers and coefficients:
  10. RHS = 9(625) - 100(25)
  11. RHS = 5625 - 2500
  12. RHS = 3125

Since LHS = RHS (3125 = 3125), x=-5 satisfies the equation.