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

5x^{2} + 13x + k = 0

D = 169 - 20k

x_{1} = (-13 + √(169 - 20k))/10

x_{2} = (-13 - √(169 - 20k))/10

x_{1 }= 1/x_{2}

(-13 + √(169 - 20k))/10 = 10/ (-13 - √(169 - 20k))

100 = (-13 + √(169 - 20k))(-13 - √(169 - 20k)) = 169 - 169 + 20k = 20k

k = 10.

D = 169 - 20k

x

x

x

(-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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