Question

If the zeros of a quadratic polynomial ax2 + bx + c are both negative, then can we say a, b and c all have the same sign? Justify your answer'

Answer 1

Yes. In such cases a, b, c will have same sign.

***Justification***
Both zeros are negative, means, product of zeros positive. So,
$\frac{c}{a} \: \: is \: \: positive$
Thus, a and c must be either both positive or negative

Both zeros are negative, means, sum of zeros also negative. So,
$\frac{ - b}{a} \: \: is \: \: negative \\ so \: \: \frac{ b}{a} \: \: is \: \: positive$
Thus, a and b must be either both positive or negative

Therefore, a, b, c will have same sign, either both positive or negative

Answer 2

Answer:

Yes it is true it is given that the zero are negative and we know that if zero are negative than the both factor will be positive which mean that the sign is positive