SOLUTION: If one root of 5x^2+13x+p=0 be reciprocal of the other then the value of p is

Question 966986: If one root of 5x^2+13x+p=0 be reciprocal of the other then the value of p is
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If the roots of are and ,
then we can "factorize" like this
,
and if we multiply the two expressions in brackets, we get
.
So, since that is true for all values of x,
the coefficients must be the equal, meaning that
,
and .
We can find those reciprocal roots,
or at least prove that there are real roots,
to make sure we have not been tricked.
It turns out that the determinant for is
and there are real roots given by
.
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