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Dinu

· started a discussion

· 1 Months ago

the root of k^2 - 24k + 144 is 12 (Question: 96235.0 )

the root of k^2 - 24k + 144 is 12. Hence answer is 122

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

Knowledge Expert

· commented

· 1 Months ago

Dear Student ,
The given answer is correct.
If roots are reciprocal of each other then their product is 1.
We know that product of roots of equation is c/a
i.e k^2 - 24k + 144 = 1
k^2 - 24k +143 = 0
(k-11)(k-13)=0
therefore k = 11,13

Thanks and Regards
Team TR

Dinu

· commented

· 1 Months ago

sorry not 122 , its 12. typing mistake
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