Question

If the equation `x^2+5kx+16=0` has no real roots then   

(a)`k>8/5`                          (b) `k(-8)/5`  

(c)` (-8)/5<k<8/5`                         (d)  None Of these

Answer 1

(c) `(-8)/5<k<8/5`  

It is given that the equation `(x^+5kx+16=0)` has no real roots.  

∴`(b^2-4ac)<` 

⇒`(5k)^2-4xx1xx16<0` 

⇒`25k^2-64<0` 

⇒`k^2<64/25` 

⇒`-8/5<k<8/5`