Question

if all the zero of the cubic polynomial are negative than all the coefficient tthan of the polynomial have the same sign state true or false justify your answer ​

Answer 1

Answer:

Let the zeroes of Cubic Polynomial be -a, -b, -c.

We can say that at x = -a, -b, -c, p(x) = 0

i.e., p(x) = (x + a)(x + b)(x + c)

Now when we multiply the above equation, we get the coefficients and constants of the polynomial to be positive.

Hence, 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.

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