Question

If $p$ and $q$ are odd integers, then the equation $x^2+2px+2q=0$

• A. has no integral root
• B. has no rational root
• C. has no irrational
• D. has no imaginary root.

Answer 1

The correct option is B has no rational root

the discriminant is

$b^2-4ac=(2p{)}^2-4\times 1\times 2q$

$=4p^2-8q$

$=4(p^2-2q)$

Since $p$ and $q$ are add integer

$p^2-2q=(2a+1{)}^2-2(2t+1)$

$=(4s^2+4s+1)-(4t+2)$

$=(4s^2+4s-4t-1)$

which is $3$ and $4$

the discriminant cannot be a perfect square so there is no rational roots