• Jan 16th 2010, 08:37 PM
matsci0000
1.Consider the equation x^2+2x-n=0, where n belongs to the set of natural numbers and n belongs to the set [5,100].The total number of different values of 'n' so that the given equation has integral roots is
a) 4 b)8 c)3 d)6

2. If b,c are odd integers , then the equation x^2+bx+c=0 has
a) two odd roots
b)two integer roots , one odd & one even
c)no integer roots
d) None of roots

• Jan 16th 2010, 09:27 PM
dedust
Quote:

Originally Posted by matsci0000
1.Consider the equation x^2+2x-n=0, where n belongs to the set of natural numbers and n belongs to the set [5,100].The total number of different values of 'n' so that the given equation has integral roots is
a) 4 b)8 c)3 d)6

2. If b,c are odd integers , then the equation x^2+bx+c=0 has
a) two odd roots
b)two integer roots , one odd & one even
c)no integer roots
d) None of roots

$\displaystyle \sqrt{1 + n}$ should be integer. For $\displaystyle n \in [5,100]$, there are 8 solutions
b) the roots are $\displaystyle x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4c}}{2}$. It can be real or imaginary numbers