Question

if the zero of polinomial x² - 3x²+x+1 and a-6, a,a+6 find a and b​

Answer 1

Answer:

a=1,b=√2.

Step-by-step explanation:

The given polynomial is x² - 3x²+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