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Find the values of k for which the following equation has equal roots: (k-12)x^2 + 2(k-12)x + 2 = 0.

Asked by Anjali Sahu 22nd March 2014, 8:47 PM
Answered by Expert
Answer:
For the equation, a x squared plus b x plus c space equals space 0, if the roots are equal then b squared minus 4 a c space equals 0
 
Hence, if the equation, (k-12)x2 + 2(k-12)x + 2 = 0 has equal roots,
then [2(k-12)]2 -4(k-12)x 2 = 0
=>4(k-12)2 -8(k-12)=0
 
=> 4(k-12)[(k-12)-2]=0   (Taking 4(k-12) common from both terms)
=>4(k-12)(k-14)=0
 
=>k-12 = 0   or k-14 = 0
 
=> k = 12 or 14
 
When k = 12, the equation becomes 0x2 + 2 x 0x + 2 = 0
=> 2 = 0, which is not possible.
 
Hence k = 14 only.    
Answered by Expert 22nd March 2014, 9:19 PM
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