Question

if one root of a polynomial p(y)=5y^2+13y+m is reciprocal of the other. then find the value of m

Answer 1

sum of roots = -b/a

product of roots = c/a

Let the roots be x , 1/x..[since one root is reciprocal of other]

x + 1/x = -13/5

x*1/x = m/5

1 = m/5

m = 5

Answer 2

Given:

P(y)=5y^2+13y+m

To find:

The value of m

Solution:

The required value of m is 5.

We know that the given polynomial's roots are reciprocal of one another.

So, let a root be X and the other root=1/X.

The given polynomial=P(y)=5y^2+13y+m

The values of the coefficients of $y^{2}$, y and the constant term are a, b, and c.

So, a=5, b=13, and c=m.

We know that the product of P(y)'s roots=c/a

Using the values,

X×1/X=m/5

X/X=m/5

1=m/5

5=m

Therefore, the required value of m is 5.