If One Root of the Polynomial p(y)=5y^2 +13y + m is Reciprocal, Find the Value of m
By BYJU'S Exam Prep
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.
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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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