Question

if one root of the equation 5x^2+13x+k=0 is the reciprocal of the other then k=?

Answer 1

because the roots are reciprocals it means there product should be 1
so from the equation
product of roots=c/a=k/5=1
=>k=5

Answer 2

Let one of the root be "t" then the other root will be "1/t"
So, product of roots = constant i.e. t × 1/t = c/a
So k /5= 1→ k = 5

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