Find the value of given equations in polynomial , Mathematics

If α & ß are the zeroes of the polynomial 2x2 - 4x + 5, then find the value of a.α2 + ß2  b. 1/ α + 1/ ß  c. (α - ß)2 d. 1/α2 + 1/ß2   e.  α3 + ß3 (Ans:-1, 4/5 ,-6, - 4/25 ,-7)

Ans: Let p(x) = 2x2 - 4x +5

α+β = - b/a = 4/2 = 2

αβ = c/a = 5/2

a)  α22 = (α+β)2 - 2αβ

Substitute to get = α22 = -1

b) 1/a + 1/β = α + β/αβ

substitute , then we get = 1/a + 1/β  = 4/5

b)  (α-β)2  = (α+β)2  - 4 αβ

Therefore we get, (α-β)2 = - 6

d)   1/α 2  +  1/β 2 = α 2  + β 2/ αβ 2 =  - 1/(5/2)2

∴   1/α 2  +  1/ β 2  = - 4/25

e)  α33  = (α+β)(α22 - αβ)

Substitute this,

to get, α33 = -7

Posted Date: 4/8/2013 2:07:57 AM | Location : United States







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