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Answer on Algebra Question for shivam

Question #2436
If one of the zeroes of the polynomial 5x2 + 13x +k is reciprocal of the other, then
find the value of k.
Expert's answer
5x2 + 13x + k = 0
D = 169 - 20k
x1 = (-13 + √(169 - 20k))/10
x2 = (-13 - √(169 - 20k))/10

x1 = 1/x2
(-13 + √(169 - 20k))/10 = 10/ (-13 - √(169 - 20k))
100 = (-13 + √(169 - 20k))(-13 - √(169 - 20k)) = 169 - 169 + 20k = 20k
k = 10.

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