Question

if all zeros of cubic polynomial are negative then all the coefficients and constant terms of a parliament have the same sign is the above statement true justify your answer​

Answer 1

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.

Answer 2

yes, The statement is true

Step-by-step explanation:

if all zeros of cubic polynomial are negative then all the coefficients and constant terms of a  polynomial  have the same sign

consider the polynomial be

ax³+bx²+cx + d = 0

and the zeroes of the polynomial be -p,-q and -r

then sum of the zeroes = $\frac{-b}{a}$

-(p+q+r) = $\frac{-b}{a}$

i.e (p+q+r) = b/a (positive)

similarly

pq +qr+rp =$\frac{c}{a}$

pqr = $\frac{d}{a}$

hence , it is concluded that  all zeros of cubic polynomial are negative then all the coefficients and constant terms of a  polynomial  have the same sign

#Learn more:

X-1/x+1 is apolynomial or not

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