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TRINA DAS

· started a discussion

· 1 Months ago

Not clear (Question:96235.0)

Please explain the 3rd line of detailed solution.

Question:
If the roots of the equation x2 + (3k - 36)x + k2 -  24k + 144 = 0 are reciprocal to each other, then find the value of k.
Options:
A) K= 11 or K= 13
B) K=-11 or K= - 13
C) K = 12
D) K= -12 
Solution:

x2 + (3k - 36)x + k2 - 24k + 144 = 0          

Since, roots are reciprocal, product of roots = 1

⇒ k2 - 24k + 144 = 1

⇒ k2 - 13k - 11k + 143 = 0

or,  K(k-13)-11(k-13) = 0

or, (k-13)(k-11)=0

So, k=11,13

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