Question

If one root of the polynomial p(y)=5y² +13y + m is reciprocal, find the value of m.

Answer 1

Sum of roots = -b/a
product of roots = c/a

Let the roots be x , $\frac{1}{x}$ [since one root is reciprocal of other]
Here in p(y)=5$y^2$ +13y + m,

we have a=5, b=13 and c=m

Sum of roots $⟶$ x + $\frac{1}{x}$ = -$\frac{13}{5}$
product of roots $⟶$ x $\times \frac{1}{x}$ = $\frac{m}{5}$
1 = $\frac{m}{5}$
m = 5

Thus, the value of m is 5.