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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
Solution
(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`
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