Question

If α, β are the zeroes of a polynomial 3xsquare+6x-1, find α+β and αβ and hence find α/β^ +β/α^.


Plzz answer
Its veryy important plzzzz

Answer 1

Question

If α, β are the zeroes of a polynomial 3x² + 6x - 1, find α+β and αβ and hence find α/β +β/α

Solution

Given :-

• Polynomial equation, 3x² + 6x - 1 = 0
• α and β are zeroes.

Find :-

• value of α+β and α.β
• Value of α/β +β/α .

Explanation

Using Formula

★ Sum of zeroes = -(Coefficient Of x )/(Coefficient of x²)

★ Product of zeroes = (Constant part)/(Coefficient of x²)

So,

==> Sum of Zeroes = -(6)/(3)

==> Sum of Zeroes = -2

==> α+β = - 2 -------------------Equ(1)

And,

==> Product of zeroes = -1/3

==> α.β = -1/3 ------------------Equ(2)

Squaring both side of equation (1)

==> (α+β)² = (- 2)²

==> α² + β² + 2α.β = 4

Keep value by equ(2)

==> α² + β² + 2* (-1/3) = 4

==> α² + β² = 5 + 2/3

==> α² + β² (5*3 + 2)/3

==> α² + β² = (15+2)/3

==> α² + β² = 17/3 ---------------------equ(3)

So, Now calculate

α/β +β/α

= (α² + β²)/α.β

Keep value by equ (2) & equ(3)

= (17/3)/(-1/3)

= 17/3 * (-3)

= -17 [ Ans]

__________________