Question

if one zero of the quadratic polynomial p (y)=
${5y }^{2} + 13y + m$

Answer 1

As products are reciprocal , their product will be =1 and we know that product of roots =c/a=m/5 then m=5

Answer 2

We know that a quadratic polynomial can have a maximum of two zeroes . We need to find the roots of the polynomial . so , let us set this equal to zero
⇒5y²+13y+m=0. here a=s , b=13 , c=m
⇒y(zeroes of p(y) )= -13+or-√(13²-4×5×m) ÷2×5
⇒y=  -13+or-√169-20m ÷10
Since the zeroes are reciprocals of themselves ,
⇒ -13+√169-20m ÷10 =10÷ -13-√169-20m. 
⇒ -13+√169-20m=100÷ -13-√169-20m.
⇒mutiplying both sides of the equation by -13-√169-20m. we get,
⇒  -13²-(169-20m)=100
⇒169-169+20m=100
⇒m=5
You can verify this by plugging m=5 in any of the above equations.


                                          THAT'S IT!