Question

please help me with this​

Answer 1

Solution

Given :-

• α & β are zeroes of equation x² + 7x + 12 = 0

Find :-

• Value of 1/α + 1/β - 2α β

Explanation

Using Formula

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

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

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So,

==> Sum of zeroes = -7/1

==> α + β = -7 -----------(1)

And,

==> Product of zeroes = 12/1

==> α β = 12 -----------(2)

Using ,

★ (a-b) = √[(a+b)² - 4ab]

So,

==> α - β = √[(α + β )² - 4αβ ]

Keep Value by equ(1) & equ(2)

==> α - β = √[(-7)² - 4*12]

==> α - β = √[49 - 48]

==> α - β = √1

==> α - β = 1 ---------------(3)

Add equ(1) & equ(2)

==> 2 α = -6

==> α = -6/2

==>α = -3

Keep Values in equ(2)

==> -3 - β = 1

==> β = -3 -1

==>β = -4

Now, Calculate Value of (1/α + 1/β - 2α β )

==> 1/α + 1/β - 2α β

Keep value of α & β

==> - 1/3 - 1/4 - 2*(-3)*(-4)

==> (-4-3)/12 - 24

==> -7/12 - 12

==> (-7- 144)/12

==> -151/12

Hence

• Value of 1/α + 1/β - 2α β will be = -151/12

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