Question

guys need helppppppp ☺️


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¿¿¿¿?​

Answer 1

Answer

In the attachment ☺️

Answer 2

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.