In a quadratic equation xsquare +kx +1= 0 ,find range of k for which both roots are A) positive B) negative C) one positive and one negative

Given quadratic equation is x² + kx + 1 = 0

Sum of roots = -k

Product of roots = 1

A) When both roots are positive, the sum as well as the product is positive.

So, we have:

-k > 0, i.e., k < 0

B) When both roots are negative, the sum is negative but the product is positive.

So, we have:

-k < 0, i.e., k > 0

 

Note: For the third case, we would request you to cross- check and clarify the condition again as there seems some problem in that.