Question

If alpha and beta are zeroes of the polynomial 2x square - 4x + 5 , then find the value of following:-
1:- alpha square + beta square
2:- 1/alpha + 1/beta

Answer 1

Answers are-:::::::

2x² - 4x +5 =0

α+β = -(-4/2) = 2

αβ = 5/2

i)α² +β² = (α+β)² - 2αβ

= (2)²- 2×(5/2) = 4-5

= -1

ii)(α-β)² = (α+β)² - 4αβ

=(2)² - 4×(5/2) = 4 - 10

= -6

Answer 2

SOLUTION:-

2x²-4x+5 ( ax²+bx+c )

a=2,b=-4,c=5

α+β= -b/a = -(-4)/2 = 4/2 = 2

α×β = c/a = 5/2

1. α²+β² = (α+β)²-2αβ

= (2)²-2×5/2

= 4-5

= -1

2. 1/α+1/β =α+β/αβ

= 2/5/2

= 4/5

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