Let a, b and c be a real numbers such that a&gt;0, b&lt;0 and c&lt;0. Find the sign of each expression. a) -b b) a+c c) c-a d) ab2

Question

Let a, b and c be a real numbers such that a&amp;gt;0, b&amp;lt;0 and c&amp;lt;0. Find the sign of each expression.  a) -b  b) a+c  c) c-a  d) ab2

yunitsiL · Accepted Answer

(a) Here b&amp;lt;0⇒−b 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 b&amp;lt;0andc&amp;lt;0⇒bc&amp;gt;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&amp;gt;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 a&amp;gt;0,c&amp;lt;0⇒c−a&amp;lt;0. Thus, sign of a-b is negative . (d) The square of ay number will be positive. Thus, b2&amp;gt;0 and given a&amp;gt;0. Thus, ab2&amp;gt;0. Therefore, the sign of ab2 is positive.

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

Answered question

Answer & Explanation

New Questions in Pre-Algebra