Find the quadratic polynomial ,the sum of whose zeroes is 5/2 and their product is 1. Hence, find the zeroes of the polynomial. About the author Arya
Answer: Given :- α+β= 2 5 αβ=1 P(x)=x 2 −(α+β)x+αβ P(x)=x 2 − 2 5 x+1 =2x 2 −5x+2 P(x)=0 2x 2 −5x+2=0 2x 2 −4x−x+2=0 2x(x−2)−1(x−2)=0 (2x−1)(x−2)=0 2x−1=0 & x−2=0 x= 2 1 & x=2 are zeros of P(x) Reply
Answer:
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Answer:
Given :-
α+β=
2
5
αβ=1
P(x)=x
2
−(α+β)x+αβ
P(x)=x
2
−
2
5
x+1
=2x
2
−5x+2
P(x)=0
2x
2
−5x+2=0
2x
2
−4x−x+2=0
2x(x−2)−1(x−2)=0
(2x−1)(x−2)=0
2x−1=0 & x−2=0
x=
2
1
& x=2 are zeros of P(x)