Discussion

Explanation:

In a polynomial ax³ + bx² + cx + d = 0, whose roots are α, β and γ.
⇒ α + β + γ = -b/a
⇒ αβ + βγ + γα = c/a
⇒ αβγ = -d/a

If roots of 5x³ + cx² – 10x + 9 = 0, r, -r and γ
⇒ r – r + γ = -c/5   
⇒ γ = -c/5   …(1)

⇒ r × -r + r × γ – r × γ = (-10)/5 = -2
⇒ r² = 2   …(2)

⇒ r × - r × γ = -(9/5)
⇒ r² × γ = 9/5
⇒ γ = 9/10   …(3)

From (1) and (3)
⇒ -c/5 = 9/10
⇒ c = -9/2

Hence, option (b).

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