# If One Root of the Polynomial p(y)=5y^2 +13y + m is Reciprocal, Find the Value of m

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Updated on: October 17th, 2023

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

To find the vaue of m, we will use the given steps:

• Step 1: Denote the two roots as α and β, with α being the reciprocal of β.
• Step 2: Identify the coefficients of the polynomial p(y): a d= 5, b = 13, and c = m.
• Step 3: Use the relationship between the coefficients and the roots of a quadratic polynomial:
The sum of the roots (α + β) is given by -b/a.
The product of the roots (α * β) is given by c/a.

Let us see the steps to find the detailed solution.

## If One Root of the Polynomial p(y) = 5y² + 13y + m is the Reciprocal of the Other Root, Find the Value of m

Let’s denote the two roots as α and β, with α being the reciprocal of β. That means αβ = 1.

We also know that for a quadratic polynomial in the form of ay² + by + c, the sum of the roots (α + β) is given by -b/a and the product of the roots (αβ) is given by c/a.

In this case, a = 5 and b = 13. We need to find the value of m.

Therefore,

αβ = 1 = m/5,

On solving, we get

m = 5

Hence, the value of m is 5.

## One Root of the Polynomial p(y) = 5y² + 13y + m is the Reciprocal of the Other Root, the Value of m is 5

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