Question

4.
Verify that 1,-1 and +3 are the zeroes of the cubic polynomial x - 3x2 - x+3 and
check the relationship between zeroes and the coefficients.​

Answer 1

Step-by-step explanation:

Let p(x)=x³+3x²−x−3

p(1)=(1)³+3(1)²−1−3=0

p(−1)=(−1)³+3(−1)²+1−3=0

p(−3)=(−3)³ +3(−3)²+3−3=0

Hence, 1,−1 and −3 are the zeroes of the given polynomial.

If α,β,γ, are roots of a cubic equation ax³+bx²+cx+d=0, then

1. α+β+γ=−b/a

2. α×β+γ×β×γ+α×γ=c/a

3. α×β×γ=−d/a

⇒−3=−b/a

−3=−3/1 =−3

⇒−1=− 1/1

−1=−1

⇒3=−(-3) /1

3=3

Hence the relationship between zeroes and coefficients is also satisfied.