Question

Verify whether 1,-1,+3 are the zeroes of the cubic polynomial x³-3x²-x+3​

Answer 1

Step-by-step explanation:

P(x)=x

3

−3x

2

−x+3

P(1)=1

3

−3(1)

2

−1+3 =1−3−1+3=4−4=0

P(−1)=(−1)

3

−3(−1)

2

−(−1)+3=−1−3+1+3=0

P(3)=3

3

−3(3)

2

−(3)+3 =27−27−3+3=0

∴α=1,β=−1 and γ=3 are the zeroes of the polynomial

ax

3

+bx

2

+cx+d=0 i.e, x

3

−3x

2

−x+3=0

for cubic polynomial having α,β,γ as zeroes

α+β+γ=

a

−b

αβ+βγ+γα=

a

c

αβγ=

a

−d

α+β+γ=1−1+3=3 and

a

−b

=

1

−(−3)

=3 [verified]

αβ+βγ+γα=1(−1)+(−1)3+3(1)=−1 and

a

c

=

1

−1

=1 [verified]

αβγ=1(−1)(3)=−3 and

a

−d

=

1

−3

=−3 [verified]