Question

if alpha and beta are the zeroes of polynomial x^2-2x+3 then find alpha^2+beta^2.

Answer 1

hello 
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If α and β are the zeros of polynomial x² - 2x + 3
then α +β = -b/a = 2 
and  αβ    = c/a   = 3
(α + β)²    = α² + β² + 2αβ
α² + β²     = (α + β)² - 2αβ 
α² + β²     = 2² - 2 x 3 
α² + β²     = 4 - 6 
α² + β²     = -2

Answer 2

Hi !

p(x) = x² - 2x + 3

α and β are zeros of p(x)

sum of zeros = α +β = -b/a = 2
Product of zeros = αβ = c/a = 3

to find:-
α² + β²
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α² + β² = (α + β)² - 2αβ

α² + β² = 2² - 2 x 3

α² + β² = 4 - 6

α² + β² = -2

Hope this Helps you !