Question

if α and β are zeroes of polynomial of the polynomial x²+x-2 find 1/α - 1β

Answer 1

Solution

Given :-

• polynomial , x² + x - 2 = 0
• α and β are zeroes of this polynomial

Find :-

• Value of 1/α - 1/β

Explanation

Using Formula,

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

★product of zeroes = (constant part)/(coefficient of x²)

★ ( α - β) = √[(α + β)² - 4α β]

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Now, calculate,

➡ Sum of zeroes = -(coefficient of x)/(coefficient of x²)

➡ (α + β) = -1 __________(1)

Again,

➡product of zeroes = (constant part)/(coefficient of x²)

➡ (α β) = -2 _____________(2)

So, Now calculate (α - β)

➡ ( α - β) = √[(α + β)² - 4α β]

keep all above values

➡ ( α - β) = √[(-1)² - 4*(-2)]

➡( α - β) = √(1+8)

➡( α - β) = √9

➡( α - β) = 3 _______________(3)

Now, calculate (1/α - 1/β)

➡ (1/α - 1/β) = ( α - β)/α β

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

➡ (1/α - 1/β) = 3/(-2)

➡ (1/α - 1/β) = -3/2

Hence

• Value of (1/α - 1/β) be = -3/2

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Answer 2

Answer:

hope this will help u ❤️