If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
By BYJU'S Exam Prep
Updated on: October 17th, 2023
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, the value of k is -⅔. Candidates should write polynomial equations in standard form before attempting to solve them. Calculate the factors and then set each variable factor to zero once they have all reached zero. The solutions to the original equations are the responses to the derived equations.
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f(t) = kt2 + 2t + 3k. Find the Value of k.
The question states If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.” The value of a variable in a polynomial may occasionally be zero. These numbers are described by polynomial zero. Sometimes people refer to them as polynomial roots. We usually determine the zeros of quadratic equations to get the solutions to the given problems.
The following is the step-by-step solution for the given problem:
Given, f(t) = kt2 + 2t + 3k
Let roots be α and β
Sum of the roots = α + β = -2/k
Product of the roots = αβ = 3k/k
According to question, α + β = αβ
-2/k = 3k/k
Hence, the value of k = -⅔.
Summary:
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
The value of k is -⅔, if the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product. Division, subtraction, multiplication, and addition are all polynomial operations. Any polynomial may be solved with ease using basic algebraic concepts and factorization strategies. Setting the value of the right-hand side of the polynomial equation to zero is the first step in solving it.
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