If alpha and beta are zeroes of the polynomial, x square -x-2. Find the value of 1/alpha square +1/ beta square.
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given polynomial :-
x² - x - 2
using splitting method to find alpha and beta.
= x² - (2x - x) - 2
= x² - 2x + x - 2
= x(x - 2) + 1(x - 2)
= (x - 2) (x + 1)
equating both factors with 0.
➡ x - 2 = 0
➡ x = 2
➡ x + 1 = 0
➡ x = -1
therefore alpha is = 2 and beta is = -1
hence, value of 1/alpha² + 1/beta² = 1/(2)² + 1/(-1)²
= 1/4 + 1/1
= 1/4
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