Verify that 1, -1 and +3 are the zeroes of the cubic polynomial x³- 3x²- x +3 and check the relationship between zeroes and the coefficients.
Answers
Answer:
1-1,+3=points 0
Step-by-step explanation:
it means you know do first learn the point of 1 2 and 3 then you need to divide one and one by then + them and the answer is your correct answer it's my step by step explanation I hope it helps you
Let zeros be α=1, β=−1, γ=−3
a) α 3+3α2−α−3
1+3−1−3=0
α is a zero
b) β 3+3β 2
−β−3
−1+3+1−3=0
β is a zero
c) γ 3+3γ2
−γ−3
−27+27+3−3−=0
γ is a zero
We know that
1)α+β+γ=
a−b
Let zeros be α=1, β=−1, γ=−3
a) α
3
+3α
2
−α−3
1+3−1−3=0
α is a zero
b) β
3
+3β
2
−β−3
−1+3+1−3=0
β is a zero
c) γ
3
+3γ
2
−γ−3
−27+27+3−3−=0
γ is a zero
We know that
1)α+β+γ=a−b
LHS=1−1−3=−3
RHS= 1−3=−3
LHS=RHS
2)αβ+βα+αγ= ac
LHS=−1+3−3
=−1
RHS=−1
LHS=RHS
3)αβγ= a−d
LHS=1(−1)(−3)=3
RHS=−( 1−3)=3
LHS=RHS
LHS=1−1−3=−3
RHS= 1−3 =−3
LHS=RHS
2)αβ+βα+αγ= ac
LHS=−1+3−3
=−1
RHS=−1
LHS=RHS
3)αβγ=
a−d
LHS=1(−1)(−3)=3
RHS=−(1−3)=3
LHS=RHS