Question

If the equation `9x^26kx+4=0`  has equal roots then k =? 

(a)1  or  (b)-1 or 4 (c)1 or -4  (d)-1 or -4 

Answer 1

(a) `1 or 4` 

It is given that the roots of the equation `(x^2+2(k+2)x+9k=0)` are equal.  

∴`(b^2-4ac)=0` 

⇒`{2(k+2)}^2-4xx1xx9k=0` 

⇒`4(k^2+4k+4)-36k=0` 

⇒`4k^2+16k+16-36=0`  

⇒`4k^2-20+16=0` 

⇒`k^2-5k+4=0` 

⇒`k^2-4k-k+4=0` 

⇒`k(k-4)-(k-4)=0` 

⇒`(k-4) (k-1)=0` 

⇒` k=4  or  k=1`