Question

if zero of polynomial X"'-3x^+X+1 are a-b,a+band a then find a and b​

Answer 1

Answer:

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Step-by-step explanation:

Answer:

a = 1

b = ±√2

step by step explanation

p(x)=x

3

−3x

2

+x+1

A standard cubic equation is of the form ax

3

+bx

2

+cx+d

On comparing the two equations, we get

a=1

b=−3

c=1

d=1

Given zeroes are:

α=a−b

β=a

γ=a+b

We know that in a cubic polynomial,

sum of zeroes = −

a

b

⟹α+β+γ=−

1

(−3)

⟹a−b+a+a+b=3

⟹3a=3

⟹a=3÷3=1

⟹

a=1

We also know that in a cubic polynomial,

Product of zeroes = −

a

c

⟹α×β×γ=−

a

c

⟹(a−b)(a)(a+b)=−

1

1

Put a = 1

(1−b)(1)(1+b)=−1

⟹1

2

−b

2

=−1

⟹1−b

2

=−1

⟹b

2

=1+1

⟹b

2

=2

b=±

2

Answer 2

Answer:

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