Question

Alpha & beta are zeroes of polynomial 2x^2-4x+5 , find the value of 1\alpha + 1\beta & 1\alpha square + 1\beta square

Answer 1

$\textbf{Hey Mate, Here is your answer}$

$\textbf{I will use 'p' for alpha and 'q' for beta}$

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$\textbf{Answer :- }$

Given, 2x ² - 4x + 5

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

p + q(Sum of roots) = -b/a

==> 4/2

p + q = 2............(1)

Next,

pq( product of roots ) = c/a

==> 5/2............(2)

( Ⅰ )

1/p + 1/q

==> p + q/pq

==> 2 ÷ 5/2

==> 2 × 2/5

==> 4/5

Therefore, 1/p + 1/q = 4/5

( Ⅱ )

1/p ² + 1/q ²

==> p ² + q ²/p ²q ²

==> (p + q) ² - 2pq/(pq) ²

==> (2) ² - 2 × 5/2 ÷ (5/2) ²

==> 4 - 5 ÷ 25/4

==> -1 × 4/25

==> -4/25

Therefore, 1/p ² + 1/q ² = -4/25

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