Question

if alpha and beta are the zeroes of polynomial f(y)=y²+y-2 , find the value of 1/alpha +1/beta?​

Answer 1

Question

If α and β are the zeroes of polynomial f(y)=y²+y-2 , find the value of 1/ α + 1/ β?

Solution

Given:-

• polynomial , f(y) = y² + y - 2 = 0 ---(1)
• α and β are zeroes .

Find:-

• Value of 1/α + 1/β .

Explanation

If Ax² + Bx + C = 0 a polynomial equation ,

Then,

☛ Sum of zeroes = -B/A

☛ Product of zeroes = C/A

So, in given equation,

• A = 1
• B = 1
• C = -2

☞ Sum of zeroes = -1/1

☞ α + β = -1 --------(1)

☞ product of zeroes = (-2)/1

☞ α.β = -2 ----------(2)

Now calculate,

➩ 1/α + 1/β

= (α + β)/α.β

keep value by equation (1) and (2),

= (-1)/(-2)

= 1/2

Or,

= 0.5

Thus:-

• Value of 1/α + 1/β = 0.5. [Ans]

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