Question

if -1 and -2 are the zeros of the cubic polynomial x cube minus x square + bx - 8 find the values of a and b​ .

Answer 1

Answer:

P(X)=X^3+3X^2+X+1

COMPARE WITH AX^3+BX^2+CX+D

A=1

B= -3

C= 1

D= 1

NOW ZEROES OF THE EQUATION ARE

\alpha =a-bα=a−b

\beta =aβ=a

γ=a+b

sum of zeroes =-B/A

\alpha +\betaα+β +γ=-B/A

a-b+a+a+b=3

3a=3

a=1

product of zeroes=C/A

\alpha \betaαβ +\betaβ γ+γ\alphaα =C/A

PUTTING VALUES OF ALPHA

AS (a-b)

BETA AS a

and gamma as (a+b)

WE GET

3a^2-b^2=1

NOW PUTTING

a=1

WE GET b AS ±\sqrt{2}

2

a=1 b=±\sqrt{2}

2

a+b=1+\sqrt{2}

2

or

a+b=1-\sqrt{2}

2