If one zero of the polynomial f(x) = (k2+4)x2 + 13x + 4k is reciprocal of the other, then k =
By BYJU'S Exam Prep
Updated on: October 17th, 2023
If one zero of the polynomial f(x) = (k2+4)x2 + 13x + 4k is the reciprocal of the other, then the value of k is 2. Before attempting to solve them, candidates should write polynomial equations in standard form. Factor it, and when all the variable factors have reached zero, set them all to zero. The answers to the derived equations are the solutions to the original equations.
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f(x) = (k2+4)x2 + 13x + 4k, Find the Value of K.
The question states If one zero of the polynomial f(x) = (k2+4)x2 + 13x + 4k is reciprocal of the other, then k is.” 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. To get the solutions to the given problems we usually determine the zeros of quadratic equations.
Let’s assume the roots of the polynomial be α, 1/α
Product of the roots of the polynomial = 4k/k2+4
α * 1/α = 4k/k2+4
4k/k2+4 = 1
4k = k2 + 4 = 1
(k – 2)2 = 0
k = 2
Hence, if one zero of the polynomial f(x) = (k2+4) x2 + 13x + 4k is the reciprocal of the other, then the value of k is 2.
Summary:
If one zero of the polynomial f(x) = (k2+4)x2 + 13x + 4k is reciprocal of the other, then k =
The value of k is 2, if one zero of the polynomial f(x) = (k2+4)x2 + 13x + 4k is the reciprocal of the other. Polynomial operations include division, subtraction, multiplication, and addition. With the use of fundamental algebraic concepts and factorization techniques, any polynomial may be solved with ease. The first step in solving the polynomial equation is to set the right-hand side’s value to zero.
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