# Let a, b and c be a real numbers such that a>0, b<0 and c<0. Find the sign of each expression. a) -b b) a+c c) c-a d) ab^2

Question
Let a, b and c be a real numbers such that a>0, b
a) -b
b) a+c
c) c-a
d) $$\displaystyle{a}{b}^{{2}}$$

2020-11-09
(a) Here $$\displaystyle{b}{<}{0}\Rightarrow−{b}$$</span> will be a positive number.
Thus, sign of -a is positive.
(b) It is known that product of two negative number will be positive.
As $$\displaystyle{b}{<}{0}{\quad\text{and}\quad}{c}{<}{0}\Rightarrow{b}{c}{>}{0}.$$
Thus, sign of bc is positive.
So a and bc positive.
It is known that sum of two positive number will be positive.
Thus, a+bc>0.
Thus, sign of a + bc is positive.
(c) It is known that when a positive number is subtracted from a negative number, the resultant number will be negative .
Here $$\displaystyle{a}{>}{0},{c}{<}{0}\Rightarrow{c}−{a}{<}{0}$$</span>.
Thus, sign of a-b is negative .
(d) The square of ay number will be positive. Thus, $$\displaystyle{b}^{{2}}{>}{0}$$ and given a>0.
Thus, $$\displaystyle{a}{b}^{{2}}{>}{0}$$.
Therefore, the sign of $$\displaystyle{a}{b}^{{2}}$$ is positive.

### Relevant Questions

Let a, b and c be a real numbers such that a>0, b<0 and c<0. Find the sign of each expression.
a) -b
b) a+c
c) c-a
d) $$ab^2$$
Let a, b and c be a real numbers such that a>0, b<0 and c<0. Find the sign of each expression.
a) -a
b) bc
c) a-b
d) ab+ac
Let a and b be positive numbers such that a < b. State whether the absolute value equation has no solution, two negative solutions, two positive solutions, or one positive and one negative solution.
|x − b| = -a
no solution
two negative solutions
two positive solutions
one positive and one negative solution
Let a and b be positive numbers such that a < b. State whether the absolute value equation has no solution, two negative solutions, two positive solutions, or one positive and one negative solution.
|x − b| = -a
no solution
two negative solutions
two positive solutions
one positive and one negative solution
Let a and b be positive numbers such that a < b. State whether the absolute value equation has no solution, two negative solutions, two positive solutions, or one positive and one negative solution.
|x − b| = -a
no solution
two negative solutions
two positive solutions
one positive and one negative solution
Let a and b be positive numbers such that a < b. State whether the absolute value equation has no solution, two negative solutions, two positive solutions, or one positive and one negative solution.
|x − b| = -a
no solution
two negative solutions
two positive solutions
one positive and one negative solution
Let M be the vector space of $$2 \times 2$$ real-valued matrices.
$$M=\begin{bmatrix}a & b \\c & d \end{bmatrix}$$
and define $$M^{#}=\begin{bmatrix}d & b \\c & a \end{bmatrix}$$ Characterize the matrices M such that $$M^{#}=M^{-1}$$