Question

If α and β are zeroes of polynomial 2x²-4x+5.Then find the value of following:
(a) α²+β²
(b) 1/α+1/β
Please answer fast ......


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Answer 1

Answer: a) -1    

               b) 4/5

Step-by-step explanation:

α and β are zeroes of polynomial 2x²-4x+5.

So equate the polynomial to 0.

2x^2 - 4x +5=0

Sum of roots = -(coefficient of x)/coefficient of x^2 = α+β

Product of roots = (constant)/coefficient of x^2 = αβ

Sum of roots=α+β=4/2=2

Product of roots = αβ = 5/2

We need to find α²+β²  which can be written as -

α²+β²=(α+β)²-2αβ

Now put values of αβ and α+β in above equation

α²+β²=(2)² - 2(5/2)

        = 4 - 5

        = -1

1/α+1/β can be written as

1/α+1/β=(α+β)/αβ -----------[ By taking LCM as αβ ]

Now we know values of α+β  and αβ , so by using those values in above equation we get -

1/α+1/β=2/(5/2)

          = 4/5