Question

α, β, γ are zeroes of cubic polynomial x³– 12x² + 44x + c. If α, β, γ are in AP, find the value of c.​

Answer 1

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Answer 2

According to the question

So, Let β=a ; α=a−d & γ=a+d

Polynomial=x

3

−12x

2

+44x+c

Sum of roots=

1

−(−12)

=12

So,a−d+a+a+d=12

3a=12

a=4

Sum of products of two consecutive roots=44.

a(a−d)+a(a+d)+(a−d)(a+d)=44

a

2

−ad+a

2

+ad+a

2

−d

2

=44

3a

2

−d

2

=44

3(4)

2

−d

2

=44

d

2

=48−44=4

d=±2

So, α=a−d=

4+2

4−2

=

6

2

β=4

β=a+d=

4−2

4+2

=

2

6

So,Product (−c)=2×4×6

=−48