Verify that 5, –2 and 
are the zeros of the cubic polynomial p(x) = 3x3 - 10x2– 27x + 10 and verify the relation between its zeros and coefficients
It is given in the question that,
p (x) = 3x3 – 10x2 – 27x + 10
Also, 5, -2 and 
are the zeros of the given polynomial
∴ p (5) = 3 (5)3 – 10 (5)2 – 27 (5) + 10
= 3 × 125 – 250 – 135 + 10
= 385 – 385
= 0
p (-2) = 3 (-2)3 – 10 (-2)2 – 27 (-2) + 10
= - 24 – 40 + 54 + 10
= - 64 + 64
= 0
And, p (
) = 3 (
)3 – 10 (
)2 – 21 (
) + 10
= 
= 
= 0
Verification of the relation is as follows:
Let us assume α = 5, β = - 2 and γ = 1/3
α + β + γ = 5 – 2 + 1/3 = 
∴ 
Also, 
+ 
+ 
= 5 (-2) + (-2) (
) + (
) (5)
= - 27/3
= - 9
∴ 
And, αβγ = 
Hence, verified
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