Question

if α and β are zeroes of x² - 4x + 1, then find the value of 1/α + 1/β - αβ.

Answer 1

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Answer 2

Solution :

Given : α and β are zeroes of x² - 4x + 1;

So, Let's find out relationship between Zeroes.

↪ Sum of Zeros = -b/a

= 4 / 1

= 4

↪ Product of Zeros = c/a

= 1/1

= 1

Now, Solving Query !

1/α + 1/β - αβ

= ( α + ß/ aß ) - aß

= α + ß - ( aß )² / aß

= 4 - ( 1 )² / 1

= 4 - 1 / 1

= 3

Therefore, Value of 1/α + 1/β - αβ is 3.