Question

If-1 is the zero of polynomial 3x²+bx+5 then value of b is ​

Answer 1

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Answer 2

Answer:a=1 and b=±

2

Step-by-step explanation:

The given polynomial is x

3

−3x

2

+x+1

As (a−b),a and (a+b) are the zeros of the given polynomial

⇒(a−b)

3

−3(a−b)

2

+(a−b)+1=0 .....(1)

⇒a

3

−3a

2

+a+1=0 ....(2)

and (a+b)

3

−3(a+b)

2

+(a+b)+1=0 .....(3)

Putting a=1 in equation (2), we get

1−3+1+1=0 or 0=0

⇒ (2) is satisfied, when a=1

∴1 is a zero of the given polynomial

Putting a=1 in (1), we get

(1−b)

3

−3(1−b)

2

+(1−b)+1=0

⇒1−b

3

−3b+3b

2

−3(1−2b+b

2

)+1−b+1=0

⇒3−4b+3b

2

−b

3

−3+6b−3b

2

=0

⇒−b

3

+2b=0

⇒−b(b

2

−2)=0

Either b=0 or b

2

−2=0

But b can not be zero

∴b

2

=2

⇒b=±

2

​

Thus, a=1 and b=±

2

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