Question

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Answer 1

Answer:

Step-by-step explanation:

Verification:

Substitute each of the values 3, -2, 1 in the given function:

f(x)=x^3 - 2x^2 - 5x + 6

f(3) = 27 - 2(9) - 5(3) + 6 = 27 - 18 - 15 + 6 = 0

Similarly,

f(-2) = f(1) = 0

Sum of zeros:

α + β + γ= - b / a    

we have the values of zeros as ( 3, -2 , 1)

taking α=3 , β = -2 and γ = 1

α + β + γ = 3 - 2 + 1 = 2      ----------------- ( 1 )

coefficients: a = 1 , b = -2 , c = -5

- b / a = -(-2) / 1 = 2            ------------------( 2 )

From ( 1 ) and ( 2 ),

α + β + γ = - b / a

Product of zeros:

αβγ = - d / a

αβγ = 3 x (-2) x 1 = -6        -----------( 3 )

- d / a = - 6 / 1 = -6 --------------( 4 )

From ( 3 ) and ( 4 ),

αβγ = - d / a

Hence, verified.