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For c to be positive, and for b to be negative, m must be negative and n must be negative.


X^2 - bx + c = (x - m)(x - n).

c is the product of m and n. If both m and n are positive, c would be positive. However b is the sum of m and n, therefore to make b negative, both m and n must be negative to ensure that the product of m and n is positive


JannetPalos

Answer:

Both m and n should be negative

Step-by-step explanation:

\((x - m)(x - n) = x^{2} -(m + n)x + mn\)

Comparing this with

\(x^{2} -bx+c\), we get,

b = m + n and c = mn

We have been given that c should be positive. So, we have two cases:

1. Both m and n should be positive and

2. Both m and n should be negative

Case 1: Both m and n are positive

If both m and n are positive, then so is mn = c.

But, note that m + n (= b) will also be positive. But, it is given that b should be negative. So, this case is not possible.

Case 2: Both m and n are negative

If both m and n are negative, then mn (= c) is positive.

Also, m + n (= b) is negative.

Hence, this is the correct case.

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