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