If one root of equation 5x^2 +13x + k = 0 is reciprocal of the other root, then what is the value of k?

Question

If log4 + log(13x+1) = log(5x+9) + 1, then what is the value of x?

Note: Assume all log represented is to the base of 10.

Answer 1

5

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As per Vieta’s theorem: x1*x2 = c/a
In our case c=k & a=5 so x1*x2=k/5
Since roots are reciprocal, x1*x2=1 => k/5=1 => k=5