Question

1) Suppose that a quadratic polynomial x^2+bx+1,b∈R has two zeros which are both real then
     which one of the following is true?
     a) b can have infinitely many values
     b) b has a unique value
     c) b has at most two distinct values
     d) b has at most four distinct values .   Explain your answer.

Answer 1

When any quadratic polynomial roots are real then; according to the property of the quadratic equation,
$b^2-4ac$ = 0
substitutiong the values of a=1; b=b; c=1
$b^2$= 4*1*1
$b^2 = 4$
$b= \sqrt{4}$
b=+_2
b=+2 or b= -2,
There fore the correct answer is 'C', B has atmost two distinct values