Question

What is the possible values of b when the difference between the roots of the equation x²+ bx+1=0 is less than √12.​

Answer 1

Answer:

Let the roots be A and B

A+B = -b/a = -b

AB = c/a = 1

Difference of roots = A-B

== (A-B)² = (A+B)²-4AB

== (-b)²-4(-1)

== (A-B)²= b²+4

A-B = √(b²+4)

if A-B<√12

√(b²+4)<√12

b²+4<12

b²-8<0

(b-2√2)(b+2√2)<0

b<2√2 and b>-2√2

Possible values of b are 2 ,1,0,-1,-2

you can ask any doubt!