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if all & zeros of a cubic polynomial x² + ax ²-bolte are positive, then at least one of a, band c is non negative .
true or false...????????
need step or else reported¿¿¿¿?
Answers
Answer
In the attachment ☺️
Step-by-step explanation:
(1). Consider the cubic polynomial
Given that all the zeroes of cubic polynomial are negative.
Let –α, –β, – γ are the negative zeroes of cubic polynomial (where α, β, γ must be positive)
From (1), (2) and (3), we have –
All the coefficients and the constant term of the polynomial have the same sign.
Hence, given statement is true.
(2). Given polynomial is –
and all the three zeroes of this polynomial are given to be positive. zeroes of the polynomial.
Since α, β, γ are positive, so a must be negative.
and since α, β, γ are positive
⇒ c is positive or non-negative
Hence, exactly one of a, b, c is non-negative.
∴ the given statement is not true.
(3) Given polynomial is –
given condition is that p(x) has equal zeroes.
∴ Value of discriminant must be zero
∴ The given statement is not true.