Math, asked by disha841, 7 months ago

9. the zeroes of the polynomial F(x)=x3 - 3x2 + 1 are a-b ,a,a+b,find a and b​

Answers

Answered by Anonymous
1

CORRECT QUESTION:

The zeroes of the polynomial f(x)=x³ - 3x²+x + 1 are a-b ,a,a+b,find a and b​

GIVEN:

f(x)=x³-3x²+x+1  

Let α,β and γ be the zeroes of the polynomial,then,

a-b=α

a=β

a+b=γ

TO FIND:

The values of a and b

SOLUTION:

Sum of zeroes of a cubic polynomial=(-coefficient of x²/coefficient of x³)

α+β+γ=[-(-3)]/1

(a-b)+a+(a+b)=3      (∵ +b and -b gets cancelled)

3a=3⇒a=1

∴a=1

Now,

Product of zeroes of a cubic polynomial= -Constant term/coefficient of x³

αβγ= -1/1          

(a-b)a(a+b)= -1

(a-b)(a+b)a= -1

(a²-b²)a= -1

(1²-b²)1= -1

1-b²= -1

√b²=√2⇒b=±√2

∴b=±√2

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