Given f(x)=2x^4+3x^3-5x^2+3x+2, if k is a non zero real root of f(x)=0, show that 1/k is also a root.?

f(x) = 2x⁴ + 3x³ - 5x² + 3x + 2

k is a non-zero real root of f(x) = 0
By Factor Theorem, f(k) = 0. Then,
2k⁴ + 3k³ - 5k² + 3k + 2 = 0

f(1/k) = 2(1/k)⁴ + 3(1/k)³ - 5(1/k)² + 3(1/k) + 2
f(1/k) = (1/k)⁴ × k⁴ × [2(1/k)⁴ + 3(1/k)³ - 5(1/k)² + 3(1/k) + 2]
f(1/k) = (1/k)⁴ × [2 + 3k - 5k² + 3k³ + 2k⁴]
f(1/k) = (1/k)⁴ × [2k⁴ + 3k³ - 5k² + 3k + 2]
f(1/k) = (1/k)⁴ × 0
f(1/k) = 0

Since f(1/k) = 0, by Factor Theorem,
1/k is also a root.