the number of pairs (a.b) for which a(x+1)²+b(x²-3x-2)+x+1=0, for which x belongs to all real numbers, is:

1. 0
2. 1
3. 2
4. infinite

 

by: kuldeep sharma

Hi!

Here is the answer to your question.

 

The given equation is a(x + 1)² + b(x² – 3x – 2) + x + 1 = 0.

Since x can assume any real value, the given equation can be rewritten as ma +nb + r = 0, where m, n, and r are arbitrary constants.

This equation ma +nb + r = 0 represents a linear equation in variables a and b. Since a linear equation has infinite solutions, therefore there are infinite solutions of the given equation.

 

That is, the ordered pair (a, b) has infinite solution.

 

Cheers!