Class 10 Math All topics Polynomials
Say true or false.
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
(a)
True
(b)
False
Correct answer: (a)
Solution:
Let is a cubic polynomial and be the roots of
Then, sum of the roots is
and sum of negative numbers is negative
Thus is positive
Product of the roots taken two at a time is

Product of two negative numbers is positive and sum of positive numbers is positive
Thus, is positive
Product of the roots is and product of three negative numbers is negative
Thus is positive.
Therefore sign of all coefficients will be positive.
Hence, the Statement is true. Connecting you to a tutor in 60 seconds.
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introduction to trigonometry
functions
some applications of trigonometry
quadratic equations
surface areas and volumes