Question

If alpha beta are the zeroes of the polynomial x2+5×+6 then1/alpha+1/beta=

Answer 1

Given eqⁿ.

x² + 5x + 6, a = 1, b = 5, c = 6

Sum of roots (α + β) = -b/a = -5/1 = -5

Product of roots (αβ) = c/a = 6/1 = 6

1/α² + 1/β² = (α² + β²)/α²β²

= {(α + β)² - 2αβ}/(αβ)²

= {(-5)² - 2(6)}/(6)²  [ a² + b² = (a + b)² - 2ab ]

= (25 - 12)/36

= 13/36