Question

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) -ab) bcc) a-bd) ab+ac

Negative numbers and coordinate plane
ANSWERED
asked 2021-03-09

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) \(ab+ac\)

Answers (1)

2021-03-10

(a) Here \(a>0\) \(\displaystyle\Rightarrow\) −a will be a negative number.
Thus, sign of -a is negative .
(b) It is known that product of two negative number will be positive.
As \(b<0\) and \(c<0\) \(\displaystyle\Rightarrow\) \(bc>0\).
Thus, sign of bc is positive.
(c) It is known that when a negative number is subtracted from a positive number, the resultant number will be positive.
Here \(a>0,b<0\) \(\displaystyle\Rightarrow\) \(a−b>0.\)
Thus, sign of a-b is positive.
(d) Here
\(a>0,b<0\) \(\displaystyle\Rightarrow\) \(ab<0\)
\(a>0,c<0\) \(\displaystyle\Rightarrow\) \(ac<0\)
So ac and bc negative.
It is known that sum of two negative number will be negative.
Thus, \(ab+ac<0.\)
Thus, sign of \(ab + ac\) is .

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