Is it correct to say that, if all the zeroes of a cubic polynomials x^3+ax^2-bx+c are positive then atleast one of a, b and c is non negative? justify ur answer.
Answers
Given : all the zeroes of a cubic polynomials x^3+ax^2-bx+c are positive
To Find : Is it correct to say that atleast one of a, b and c is non negative?
Solution:
x³+ax²-bx+c
all the zeroes are positive
Hence sum of all zero is + ve
Sum of Product of two zeros taken together is + ve
Product of all zero is + ve
sum of all zero = - a/1 = - a Hence a must be negative
Sum of Product of two zeros taken together = -b/1 = - b hence b must be negative
Product of all zero = - c/1 = - c Hence c must be negative
all a , b & c must be negative
It is not correct to say that atleast one of a, b and c is non negative
as all are negative
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